Mathematical Analysis

The scientific activity of the Group “Mathematical Analysis” is focused on different subjects in the area of Calculus of Variations, Geometric Measure Theory, Fluid Dynamics, Dispersive equations, Nonlinear Analysis, Ergodic Theory, and Dynamical Systems.
Our research mainly contributes to Pure Mathematics but provides also several applications in the natural and applied sciences, e.g., Physics, Biology, and Mechanics.
The group works in close collaboration with members of the Faculty of Sciences of Scuola Normale Superiore and  Centro di Ricerca Matematica Ennio De Giorgi.

The group runs a Seminar Series: further information may be found here.

Research Topics

Calculus of variations and geometric measure theory 

The research of a large portion of the group “Mathematical Analysis” is focused on the Calculus of Variations and Geometric Measure Theory. The list of research directions includes shape and spectral optimization, free boundary problems, isoperimetric problems and related stability estimates, local and non-local geometric flows, the structure of measures and differentiability, analysis and geometric measure theory in non-Euclidean settings.
A relevant part of the research in this area is devoted to the application of Calculus of Variations and Geometric Measure Theory to problems in Mathematical Physics, Continuum Mechanics, and other areas of Mathematics.

This group has strong connections with Scuola Normale Superiore and Centro De Giorgi.
The repository CVGMT collects preprints in this area, as well as information about seminars and conferences.

Faculty Members Involved:
  • Giovanni Alberti
  • Giuseppe Buttazzo
  • Maria Stella Gelli
  • Massimo Gobbino
  • Valentino Magnani
  • Matteo Novaga
  • Emanuele Paolini
  • Alessandra Pluda
  • Aldo Pratelli
  • Vincenzo Maria Tortorelli
  • Dario Trevisan
  • Bozhidar Velichkov
Postdoctoral Fellows:
  • Roberto Ognibene
  • Giorgio Tortone
Ph.D. Students:
  • Konstantinos Bessas
  • Luca Briani Medeiros Dos Santo
  • Luciano Sciaraffia
Free boundary problems 

The free boundary problems are PDE problems (often elliptic or parabolic) in which the domain of the solution is not a priori prescribed but is part of the variables of the problem. The boundary conditions are overdetermined and might involve the trace of the function, its gradient (or just the normal derivative), and the curvature of the boundary. Solutions to free boundary problems are obtained for instance from the minimization of variational functionals that take into account both the state function (the solution of the PDE) and its domain of definition. Well-known examples of free boundary problems are the one-phase and the two-phase Bernoulli problems, the obstacle problem, the thin-obstacle problem, the optimal partitions problems, Mumford-Shah, free transmission problems, and their parabolic counterparts, for instance, the Stefan problem.

The focus is on the free boundary regularity theory, which is the study of the fine local structure of the free boundary and relates to the analysis of the interplay between the geometry of the domain and the behavior of the state function (the solution of the PDE). Of particular interest are theorems that guarantee (under some geometric conditions) that the boundary is a smooth manifold (the so-called epsilon-regularity theorems) and the analysis of the free boundaries around singularities. The methods include blow-up analysis, monotonicity formulas, density estimates, estimates on the dimension of the singular set, viscosity solutions, analysis of the stable cones, improvement-of-flatness methods, epiperimetric inequalities.

The free boundary problems are strongly related to problems in Geometric Analysis as the regularity of area-minimizing surfaces and currents; in Elliptic PDEs, for instance to the analysis of the nodal sets to the solutions of PDEs or the behavior at the boundary of the solutions (Boundary Harnack inequalities); and also to some Shape Optimization problems.

Members:
  • Roberto Ognibene
  • Giorgio Tortone
  • Bozhidar Velichkov
Collaborators:
  • Guido De Philipps (New York University)
  • Dario Mazzoleni (Università di Pavia)
  • Luca Spolaor (University of California San Diego)
  • Susanna Terracini (Università di Torino)
Geometric flows

The idea of deforming a geometric object by means of a parabolic PDEs to simplify it (e.g. to reduce its topological complexity or to make it more symmetric) goes back to Eells and Sampson who introduced the first geometric evolution equation: the harmonic map flow. Since 1964, geometric flows have been applied to a variety of topological, analytical, and physical problems, giving in some cases very fruitful results.

Among other geometric equations, we mention the mean curvature flow. This flow can be regarded as the gradient flow of the area functional: an n-dimensional time-dependent surface evolves with normal velocity its mean curvature, at any point and time. In place of the area functional, one may consider generalized perimeters, such as the fractional perimeter, and the corresponding gradient flows. Concerning the study of these flows, we are interested in the long-time existence of (weak and strong) solutions and in the classification of possible singularities. Besides the urge to introduce a non-local version of mean curvature flow, one wants also to extend it to the more singular geometric objects.

Motived by the study of grain boundaries, Brakke introduces the first weak versions of the flow and in the years a plethora of weak definitions (level set approach, minimizing movements, thresholding scheme, canonical Brakke flow) has been developed, but the one-dimensional version of this problem is also studied in the framework of classical PDEs. In such a situation the flow is called network flow.

We are interested in several aspects of evolution: well-posedness, long-time behavior, analysis of singularities, flow past singularities, and stability. Our main goal is to exploit the known results to a higher dimension.

Members:
  • Matteo Novaga
  • Alessandra Pluda
Collaborators:
  • Antonin Chambolle (CEREMADE, CNRS 7534 – Université Paris-Dauphine)
  • Annalisa Cesaroni (Università di Padova)
  • Carlo Mantegazza (Università di Napoli)
  • Rafe Mazzeo (Stanford University)
  • Massimiliano Morini (Università di Parma)
  • Marcello Ponsiglione (Sapienza Università di Roma)
  • Marco Pozzetta (Università di Napoli)
  • Mariel Saez (Pontificia Universidad Católica de Chile)
Geometric measure theory   

The development of Geometric Measure Theory (GMT) began about one hundred years ago, with the first intrinsic notions of dimension for general sets, which could be possibly non-integer, and the corresponding intrinsic notions of measure, where “intrinsic” means that it does not rely on parametrizations.
In the second half of the last century, one of the driving problems was the existence of d-dimensional surfaces with minimal area and prescribed boundary (Plateau problem), which led to the development of several “weak” notions of surface, such as finite perimeter set (Caccioppoli, De Giorgi), integral currents (Federer and Fleming), and varifolds (Almgren).

In the past fifty years these notions played a fundamental role in the treatment of many problems of geometric nature besides minimal surfaces, from the asymptotic behavior of singular perturbations problems in continuum mechanics and physics (e.g, scalar and vector models of Ginzburg-Landau type) to the notions of weak solutions of geometric evolution problems (e.g., the mean curvature flow).

At the same time, many attempts have been made to extend these theories to various non-Euclidean settings (sub-Riemannian manifolds and metric spaces with bounds on curvature). These attempts have led to several fundamental questions that have not yet been fully answered–indeed in many cases our understanding is still quite limited.

The Italian mathematical community in Calculus of Variations and Geometric Measure Theory, whose origins can be traced back to the work of Ennio De Giorgi here in Pisa, gave essential contributions to the developments mentioned above. Among the topics currently studied in our department, we mention the following:

  • GMT in sub-Riemannian manifolds: area formulas, contact sets, currents;
  • Minimal partitions;
  • Gauss-Green formulas, sets of finite perimeter and rectifiability in stratified Lie groups;
  • Weak solutions to geometric evolution problems;
  • Structure of measures and differentiability of Lipschitz functions.
Members:
  • Giovanni Alberti
  • Valentino Magnani
  • Matteo Novaga
  • Emanuele Paolini
  • Vincenzo Maria Tortorelli
Collaborators:
  • Marianna Csornyei (University of Chicago)
  • Andrea Marchese (Università di Trento)
  • Annalisa Massaccesi (Università di Padova)
  • David Preiss (Warwick University)
  • Eugene Stepanov (Steklov Institute, Saint Petersburg)
Shape optimization

The field of shape optimization had very strong growth in the last decades, mainly due to the several applications in engineering, but also for the mathematical interest related to several problems in spectral geometry. The goal is to find a domain $\Omega$ that minimizes a given cost functional, that may involve geometrical quantities as perimeter or measure, as well as other quantities related to PDEs like for instance the related energies or eigenvalues. Showing the existence of optimal shapes, and their regularity is often a very challenging issue that needs the development of new and deep tools. 

Members:
  • Luca Briani Medeiros Dos Santo
  • Giuseppe Buttazzo
  • Aldo Pratelli
Collaborators:
  • Michiel van den Berg (University of Bristol)
  • Guy Bouchitté (Université de Toulon)
  • Lorenzo Brasco (Università di Ferrara)
  • Juan Casado Diaz(Universidad de Sevilla)
  • Thierry Champion (Université de Toulon)
  • Luigi De Pascale (Università di Firenze)
  • Faustino Maestre (Universidad de Sevilla)
  • Francesca Agnese Prinari (Department of Agricultural, Environmental and Food Sciences, Università di Pisa)
PDEs, ODEs, and dynamical systems
Faculty Members Involved:
  • Jacopo Bellazzini
  • Luigi Carlo Berselli
  • Carlo Carminati
  • Elisabetta Chiodaroli
  • Luigi Forcella
  • Stefano Galatolo
  • Marco Gipo Ghimenti
  • Marina Ghisi
  • Massimo Gobbino
  • Carlo Romano Grisanti
  • Francesco Grotto
  • Vladimir Simeonov Gueorguiev
  • Pietro Majer
  • Claudio Saccon
  • Nicola Visciglia
Ph.D. Students:
  • Daniele Barbera
  • Mario Rastrelli
Dynamical systems and ergodic theory 

Our research focuses on the statistical properties of deterministic and random dynamical systems.

These studies have a wide range of applications, from a number of theoretical and geometrical questions to the understanding of the behavior of models of real-world phenomena like the dynamics of fluids, the evolution of climate and its extreme events, the dynamics of extended systems in a mean-field coupling and other complex systems. The methods used in this research are often related to probability, functional analysis, transport, and geometric measure theory.

Our research also focused on reliable computational tools for the study of the statistical properties of dynamics, computer-aided proofs, and their relation to theoretical computer science.

Members:
  • Carlo Carminati
  • Stefano Galatolo
  • Francesco Grotto
  • Leonardo Roveri
Fluid dynamics equations  

Our research focuses on the pure and applied aspects of mathematical fluid dynamics of Newtonian and non-Newtonian fluids.

The research interests span from the most theoretical questions of existence, uniqueness, and regularity of weak solutions towards applications to the numerical analysis of such flows (with finite element/differences methods) and to the study of turbulent flows, with applications to geophysical problems. The methods we use stem from those of classical analysis of PDEs in Sobolev spaces, but for the problems we consider we are using also: convex integration, analysis in Orlicz, weighted spaces, and approximate methods like reduced-order ones. More specifically for the Equations of classical fluid mechanics: incompressible Euler and Navier-Stokes equations. Existence, uniqueness, properties, and regularity of weak and suitable solutions.

Concerning non-Newtonian fluids, we are interested in the existence, regularity, numerical approximation, and long-time behavior of classes of p-fluids or electrorheological ones.

For the turbulent flows, we study the mathematical properties and the mathematical modeling of such methods, having in mind the application to the study of boundary layers and air-sea interaction, together with other multi-phase problems arising in the study of volcanic eruptions.

Collaborators:
  • Camillo De Lellis (Princeton)
  • Eduard Feireisl (Prague)
  • Ondrej Kreml (Prague)
  • Roger Lewandowski (Rennes)
  • Paolo Maremonti (Caserta)
  • Francesca Crispo (Caserta)
  • Michael Ruzicka (Freiburg)
  • Emil Wiedemann (Ulm)
Hyperbolic Equations, dispersive equations, and Kirchhoff equations   
Members:
  • Daniele Barbera
  • Jacopo Bellazzini
  • Luigi Forcella
  • Marina Ghisi
  • Vladimir Simeonov Gueorguiev
  • Mario Rastrelli
  • Nicola Visciglia
Collaborators:
  • Nicolas Burq (Université de Paris-Saclay)
  • Tohru Ozawa (Waseda University)
  • Fabrice Planchon (Université de Paris Sorbonne)
  • David Ruiz (Granada University)
  • Nikolay Tzvetkov (ENS Lyon)
  • Dinh Van Duong (ENS Lyon)
Nonlinear analysis 

The nonlinear analysis group focuses on partial differential equations of elliptic and hyperbolic types in which the presence of the nonlinear term is crucial for the existence and qualitative properties of solutions.

The research interests span from nonlinear Schroedinger equations and Gross-Pitaevskij in a Euclidean setting to Yamabe problems on compact manifolds. The main topics of the research concerning elliptic equations are the existence and multiplicity of concentrated solutions, qualitative properties, blow-up analysis, and compactness of solutions. On the time-dependent side, we focus on the existence of solitons, stability and instability issues, and long-time dynamics for equations of physical interest. Another field of research is related to functional inequalities in presence of nonlocal terms: the existence of maximizers and the role of symmetry.

Members:
  • Jacopo Bellazzini
  • Marco Gipo Ghimenti
  • Pietro Majer
Collaborators:
  • Enno Lenzmann
  • Vitali Moroz
  • David Ruiz
  • Louis Jeanjean
  • Anna Maria Micheletti
  • Angela Pistoia
  • Pietro d’Avenia
  • Simone Dovetta
  • Monica Clapp
  • Jean Van Schaftingen

Members

Staff
NameSurname Links Personal Card
GiovanniAlberti[Google Scholar] [Mathscinet]
JacopoBellazzini[Google Scholar] [Mathscinet] [Orcid]
Luigi CarloBerselli[Google Scholar] [Mathscinet] [Orcid]
GiuseppeButtazzo[Google Scholar] [Mathscinet] [Orcid]
CarloCarminati[arXiv] [Mathscinet] [Orcid]
ElisabettaChiodaroli[Google Scholar] [Mathscinet] [Orcid]
LuigiForcella[Google Scholar] [Mathscinet] [Orcid]
StefanoGalatolo[Google Scholar] [Mathscinet] [Orcid]
Maria StellaGelli[Mathscinet]
Marco GipoGhimenti[Google Scholar] [Mathscinet] [Orcid]
MarinaGhisi[Mathscinet] [Orcid]
MassimoGobbino[Mathscinet] [Orcid]
Carlo RomanoGrisanti[Google Scholar] [Mathscinet]
FrancescoGrotto[Google Scholar] [Mathscinet]
Vladimir SimeonovGueorguiev[Mathscinet] [Orcid]
ValentinoMagnani[Mathscinet]
PietroMajer[Mathscinet]
MatteoNovaga[Google Scholar] [Mathscinet] [Orcid]
EmanuelePaolini[Google Scholar] [Mathscinet] [Orcid]
AlessandraPluda[Google Scholar] [Mathscinet] [Orcid]
AldoPratelli[Mathscinet] [Orcid]
GiuseppePuglisi[Mathscinet]
ClaudioSaccon[Mathscinet] [Orcid]
Vincenzo MariaTortorelli[Mathscinet]
BozhidarVelichkov[Google Scholar] [Mathscinet] [Orcid]
NicolaVisciglia[Mathscinet]
Postdoctoral Fellows
NameSurname Links Personal Card
DiegoBerti[Google Scholar] [Mathscinet]
GiuliaBevilacqua[Google Scholar] [Mathscinet]
RobertoOgnibene[Mathscinet] [Orcid]
GiorgioTortone[Google Scholar] [Mathscinet] [Orcid]
Ph.D. Students
NameSurname Links Personal Card
DanieleBarbera
Konstantinos Bessas
LucaBriani Medeiros Dos Santo[Mathscinet]
MarioRastrelli
LucianoSciaraffia
Past Ph.D. Students
2021
  • Obinna Kennedy Idu (Università di Pisa), “Higher-Order Rectifiability Criteria And a Model for Soap Films”, supervised by Giovanni Alberti.
  • Kosuke Kita (Università di Pisa and Waseda University, Tokyo, Japan), “A study on the qualitative theory of solutions for some parabolic equations with nonlinear boundary conditions”, supervised by Vladimir S. Gueorguiev and Tohru Ozawa.
  • Luigi Marangio (Université de Bourgogne Franche-Comté), “Rigorous computational methods for understanding behavior of random dynamical systems”, supervised by Stefano Galatolo and Christophe Guyeux.
2020
  • François Générau (Université Grenoble Alpes), “On a stable variational approximation of the cut locus, and a non-local isoperimetric problem”, supervised by Bozhidar Velichkov and Édouard Oudet.
  • Andrea Merlo (Scuola Normale Superiore di Pisa), “Geometry of 1-codimensional measures in Heisenberg groups”, supervised by Giovanni Alberti and Roberto Monti.
  • Dinh Duong Nguyen (Université Rennes), “Some results on Turbulent models”, supervised by Roger Lewandowski and Luigi Berselli.
  • Marco Pozzetta (Università di Pisa), “Willmore-type Energies of Curves and Surfaces”, supervised by Matteo Novaga.
  • Baptiste Trey (Université Grenoble Alpes), “Existence and regularity of optimal shapes for some spectral optimization problems”, supervised by Bozhidar Velichkov and Emmanuel Russ.
2019
  • Francesco Bartaloni (Università di Pisa), “Infinite horizon optimal control problems with non-compact control space. Existence results and dynamic programming” supervised by Paolo Acquistavate and Fausto Gozzi.
  • Giacomo Del Nin (Università di Pisa), “A Some asymptotic results on the global shape of planar clusters”, supervised by Giovanni Alberti.
  • Valerio Pagliari (Università di Pisa), “Aymptotic behaviour of rescaled nonlocal functionals and evolutions”, supervised by Matteo Novaga.
2018
  • Ricardo Bioni Liberalquino (Univ. Fed. Rio de Janeiro) “Computation of stationary densities of systems with additive noise”, supervised by Maria Jose Pacifico.
  • Dayana Pagliardini (Scuola Normale Superiore di Pisa), “Fractional minimal surfaces and Allen-Cahn equations”, supervised by Andrea Malchiodi and Matteo Novaga.
  • Harish Shrivastava (Università di Pisa), “Shape optimisation problems for integral functionals and regularity properties of optimal domains”, supervised by Giuseppe Buttazzo.
2017
  • Luigi Forcella (Scuola Normale Superiore di Pisa), “Asymptotic problems for some classes of dispersive PDEs”, supervised by Nicola Visciglia.
  • Anna Rita Giammetta (Università di Pisa), “Perturbed Hamiltonians in one dimension: analysis for linear and nonlinear Schrödinger problems”, supervised by Vladimir Gueorguiev.
2016
  • Matteo Cerminara (Scuola Normale Superiore di Pisa), “Modeling dispersed gas–particle turbulence in volcanic ash plumes”, supervised by Luigi Berselli and Tomaso Esposti Ongaro.
  • Francois Dayrens (Université de Lyon), “Minimisations sous contraintes et flots du périmètre et de l’énergie de Willmore”, supervised by Simon Masnou and Matteo Novaga.
  • Augusto Gerolin (Università di Pisa), “Multimarginal optimal transport and potential optimization problems for Schrödinger operators”, supervised by Giuseppe Buttazzo.
  • Anna Rita Giammetta (Università di Pisa) , “Perturbed Hamiltonians in one dimension: analysis for linear and nonlinear Schrödinger problems”, supervised by Vladimir S. Gueorguiev.
  • Alessandra Pluda (Università di Pisa), “Minimal and Evolving Networks”, supervised by Matteo Novaga.
  • Emanuela Radici (FAU Erlangen-Nürnberg ), “Diffeomorphic approximation of planar elastic deformations”, supervised by Aldo Pratelli.
  • Andrea Tamagnini (Università di Firenze) “Planar Clusters”, supervised by Emanuele Paolini
  • Florian Zeisler (FAU Erlangen-Nürnberg ), “On the optimal transport problem with relativistic cost”, supervised by Aldo Pratelli.
2015
  • Marco Caroccia (Università di Pisa), “On the isoperimetric properties of planar $N$-clusters”, supervised by Giovanni Alberti.
  • Rafael Lucena (Univ. Fed. Rio de Janeiro), “Spectral Gap for Contracting Fiber Systems and Applications”, supervised by Stefano Galatolo and Maria Jose Pacifico.
2014
  • Serena Guarino Lo Bianco (Università di Pisa), “Some optimization problems in mass transport theory”, supervised by Giuseppe Buttazzo.
  • Annalisa Massaccesi (Scuola Normale Superiore di Pisa), “Currents with coefficients in groups, applications, and other problems in Geometric Measure Theory”, supervised by Giovanni Alberti.
  • Dario Mazzoleni, (FAU Erlangen-Nürnberg and Università di Pavia), “Existence and regularity results for solutions of spectral problems”, supervised by Aldo Pratelli.
2013
  • Xin Yang Lu (Scuola Normale Superiore di Pisa), “Geometric and regularity properties of solutions of some problems related to the average distance functional”, supervised by Giuseppe Buttazzo.
  • Andrea Marchese (Università di Pisa), “Two applications of the theory of currents”, supervised by Giovanni Alberti.
  • Berardo Ruffini (Scuola Normale Superiore di Pisa), “Optimization problems for solution of elliptic equations and stability issues”, supervised by Giuseppe Buttazzo.
  • Matteo Scienza (Università di Pisa), “Differentiability properties and characterization of H-convex functions”, supervised by Valentino Magnani.
  • Bozhidar Velichkov (Scuola Normale Superiore di Pisa), “Existence and regularity results for some shape optimization problems”, supervised by Giuseppe Buttazzo.
2012
  • Minh Nguyet Mach (University of Pisa), “Weak solutions to rate-independent systems: existence and regularity”, supervised by Giovanni Alberti.
  • Stefano Spirito (Univesità del L’Aquila), “The artificial compressibility approximation and the inviscid limit for the incompressible Navier-Stokes equations”, supervised by Pierangelo Marcati and Luigi Berselli.
2011
  • Al-hassem Nayam (Università di Pisa), “Shape optimization problems of higher codimension”, supervised by Giuseppe Buttazzo.
2010
  • Lorenzo Brasco (Università di Pisa), “Geodesics and PDE methods in transport models”, supervised by Giuseppe Buttazzo, Guillaume Carlier, Filippo Santambrogio.
  • Jimmy Alfonso Mauro (Università di Pisa), “Some analytic questions in mathematical physic problems”, supervised by Vladimir S. Gueorguiev.
2008
  • Davide Catania (Università di Pisa), “Linear and nonlinear wave equations”, supervised by Vladimir S. Gueorguiev.
  • Mathieu Hoyrup (ENS Paris and Universite Paris Diderot-Paris VII), “Computability, Randomness and Ergodic Theory on Metric Spaces”, supervised by Stefano Galatolo and G. Longo.
  • Cristobal Rojas (ENS Paris and École Polytechnique), “Randomness and Ergodic Theory: an Algorithmic point of view”, supervised by Stefano Galatolo and G. Longo.
2006
  • Alessio Brancolini (Scuola Normale Superiore di Pisa), “Optimization problems for transportation networks”, supervised by Giuseppe Buttazzo.
  • Angel Ivanov (Università di Pisa), “Nonlinear evolution equations in mathematical physics”, supervised by Vladimir S. Gueorguiev.
  • Filippo Santambrogio (Scuola Normale Superiore di Pisa), “Variational problems in transport theory with mass concentration”, supervised by Giuseppe Buttazzo.
  • Mirko Tarulli Di Giallonardo (Università di Pisa), “Smoothing-Strichartz estimates for dispersive equations perturbed by a first-order differential operator”, supervised by Vladimir S. Gueorguiev.
2005
  • Niccolò Desenzani (Università di Milano), “Variational convergence of Ginzburg-Landau functionals with supercritical growth”, supervised by Giovanni Alberti and Ilaria Fragalà.
  • Luca Granieri (Università di Pisa), “Mass transportation problems and minimal measures”, supervised by Giuseppe Buttazzo.
  • Stefano Zappacosta (Università de L’Aquila), “Resolvent estimates and dispersive estimates for the wave equation with potential”, supervised by Vladimir S. Gueorguiev.
2004
  • Andrea Davini (Università di Pisa), “Finsler metrics in optimization problems and Hamilton-Jacobi equations”, supervised by Giuseppe Buttazzo.
  • Michele Gori (Università di Pisa), “Lower semicontinuity and relaxation for integral and supremal functionals”, supervised by Giuseppe Buttazzo.
  • Nicola Visciglia (Scuola Normale Superiore di Pisa), “a priori estimates for the linear and semilinear perturbed wave equation”, supervised by Vladimir S. Gueorguiev.
2003
  • Francesca Prinari (Università di Pisa), “Calculus of variations for supremal functionals”, supervised by Giuseppe Buttazzo.
2001
  • Luigi De Pascale (Università di Pisa), “Morse-Sard theorem in Sobolev spaces, transport problems and applications”, supervised by Giuseppe Buttazzo and Giovanni Alberti.
2000
  • Ilaria Fragalà (Università di Pisa), “Tangential calculus and variational integrals with respect to a measure”, supervised by Giuseppe Buttazzo.
1999
  • Ariela Briani (Università di Pisa), “Hamilton-Jacobi-Bellman equations and $\Gamma$-convergence for optimal control problems”, supervised by Giuseppe Buttazzo.
1998
  • Paola Trebeschi (Università di Pisa), “Esistenza di soluzioni in problemi di ottimizzazione di forma e ostacoli”, supervised by Giuseppe Buttazzo.
1996
  • Marino Belloni (Università di Pisa), “Rilassamento di problemi variazionali con fenomeno di Lavrentiev”, supervised by Giuseppe Buttazzo.
1994
  • Loris Faina (SISSA – Trieste), “Some nonconvex variational problems in BV spaces”, supervised by Giuseppe Buttazzo.
  • Lorenzo Freddi (Università di Pisa), “Rilassamento e convergenza di problemi di controllo ottimo”, supervised by Giuseppe Buttazzo.
External Collaborators
NameSurname Links Personal Card
PaoloAcquistapace[Mathscinet]
HugoBeirao da Veiga[Mathscinet] [Orcid]
FerruccioColombini[Mathscinet]
PlacidoLongo[Mathscinet]
AntonioMarino[Mathscinet]
Anna MariaMicheletti[Mathscinet]
SergioSpagnolo[Mathscinet]
AntonioTarsia[Google Scholar] [Mathscinet]

Grants

Current
  • Variational approach to the regularity of the free boundaries (H2020-EU.1.1. - Excellent Science - European Research Council (ERC))

    Principal Investigator: Bozhidar Velichkov

    Project period: 01/06/2020 - 31/05/2025

  • Hamiltonian and dispersive PDEs (Prin 2020)

    Principal Investigator: Massimiliano Berti (SISSA, Trieste) | Coordinator of the Research Unit: Nicola Visciglia

    Members of the Research Unit: Jacopo Bellazzini, Vladimir S. Gueorguiev, Marina Ghisi, Scipio Cuccagna, Daniele Barbera, Kosuke Kita

    Project period: 22/03/2022 - 21/03/2025

  • Nonlinear evolution PDEs, fluid dynamics and transport equations: theoretical foundations and applications (Prin 2020)

    Principal Investigator: Stefano Bianchini (SISSA, Trieste) | Coordinator of the Research Unit: Luigi Carlo Berselli

    Project period: 22/03/2022 - 21/03/2025

  • GeoDom – Geometric evolution problems and PDEs on variable domains (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

    Principal Investigator: Bozhidar Velichkov

    Members of the Research Unit: Marina Ghisi, Massimo Gobbino, Emanuele Paolini, Alessandra Pluda, Francesca Agnese Prinari

    Project period: 10/10/2022 - 31/12/2024

  • Nonlinear dispersive equations and dynamics of fluids (Progetti di Ricerca di Ateneo (PRA) 2022-2023)

    Coordinator of the Research Unit: Jacopo Bellazzini

    Members of the Research Unit: Elisabetta Chiodaroli, Marco Gipo Ghimenti, Carlo Romani Grisanti, Nicola Visciglia

    Project period: 10/10/2022 - 31/12/2024

  • Gradient flows, Optimal Transport and Metric Measure Structures (Prin 2017)

    Principal Investigator: Luigi Ambrosio (SNS, Pisa) | Coordinator of the Research Unit: Giuseppe Buttazzo

    Project period: 01/08/2019 - 19/02/2023

  • Variational methods for stationary and evolution problems with singularities and interfaces (Prin 2017)

    Principal Investigator: Gianni Dal Maso (SISSA, Trieste) | Coordinator of the Research Unit: Giovanni Alberti

    Members of the Research Unit: De Luca (CNR, Roma), Maria Stella Gelli, Matteo Novaga

    Project period: 01/08/2019 - 19/02/2023

  • Nuovi sviluppi per minimi dell’energia in problemi di ottimizzazione di forma (Progetti di Ricerca di Ateneo (PRA) 2020 - 2021)

    Coordinator of the Research Unit: Aldo Pratelli

    Members of the Research Unit: Giovanni Alberti, Konstantinos Bessas, Giuseppe Buttazzo, Maria Stella Gelli, Matteo Novaga, Alessandra Pluda, Vincenzo Scattaglia

    Project period: 07/07/2020 - 31/12/2022

Past
  • Problemi di ottimizzazione e di evoluzione in ambito variazionale (Progetti di Ricerca di Ateneo (PRA) 2017 - 2018)

    Coordinator of the Research Unit: Matteo Novaga

    Project period: 10/04/2017 - 09/04/2019

Visitors

Current
First Name Last Name Affiliation Building Office
Eugene Stepanov St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences A Piano 2, 404
Past
2022
First Name Last Name Affiliation From To
Giulia Bevilacqua Politecnico di Torino Feb 20, 2022 Feb 23, 2022
Juan Casado-Diaz Universidad de Sevilla Nov 28, 2022 Dec 02, 2022
Cristiana De Filippis Università di Parma Apr 10, 2022 Apr 13, 2022
Max Engelstein University of Minnesota Sep 22, 2022 Sep 25, 2022
Davide Faranda LSCE laboratory, University of Paris-Saclay Oct 16, 2022 Oct 22, 2022
Tom Ilmanen ETH Zürich Nov 13, 2022 Nov 23, 2022
Roger Lewandowski IRMR, Université de Rennes Oct 17, 2022 Oct 20, 2022
Faustino Maestre Universidad de Sevilla Nov 28, 2022 Dec 02, 2022
Edoardo Mainini Università di Genova May 16, 2022 May 19, 2022
Annalisa Massacesi Università di Padova Sep 18, 2022 Sep 23, 2022
Dario Mazzoleni Università di Pavia Apr 03, 2022 Apr 08, 2022
Mickael Nahon Université de Savoie Jan 16, 2022 Jan 29, 2022
Nicola Soave Politecnico di Milano Mar 08, 2022 Mar 10, 2022
Eugene Stepanov St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences Oct 01, 2022 Dec 31, 2022
Salvatore Stuvard Università di Milano Statale May 22, 2022 May 27, 2022
Yoshihiro Tonegawa Tokyo Institute of Technology Nov 14, 2022 Nov 25, 2022
Hui Yu National University of Singapore Oct 11, 2022 Oct 15, 2022
2021
First Name Last Name Affiliation From To
Alessandro Audrito ETH Zürich Oct 25, 2021 Oct 28, 2021
Ekaterina Mukoseeva University of Helsinki Sep 10, 2021 Sep 24, 2021
Mickael Nahon Université de Savoie Jul 04, 2021 Jul 10, 2021
Luca Spolaor University of California San Diego Dec 05, 2021 Dec 09, 2021
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