SEMINARI DI CALCOLO DELLE VARIAZIONI

Purely unrectifiable metric spaces and perturbations of Lipschitz functions

Relatore: 
David Bate
Abstract. We give characterisations of purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of Lipschitz functions $f\colon X \to R^m$. In one such characterisation it is shown that, if $S$ has positive lower density almost everywhere, a typical $f$ (with respect to the supremum norm) has ${\mathcal H}^n(f(S))=0$. Conversely, if $E\subset X$ is $n$-rectifiable with ${\mathcal H}^n(E)>0$, a typical $f$ has ${\mathcal H}^n(f(E))>0$.
Data Seminario: 
Wednesday, May 23, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Helsinki
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Structured deformations of continua: theory and applications

Relatore: 
Marco Morandotti
Abstract. Structured deformations provide a multiscale geometry that captures the contributions at the microlevel of both smooth geometrical changes and disarrangements at submicroscopic levels. Due to this versatility, they turn out to be a powerful tool to describe the deformations of bodies in a variety of settings. In this seminar, I will present the basic theory of structured deformations, alongside with some applications.
Data Seminario: 
Wednesday, April 18, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
TUM Monaco
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Limiting behaviour of rescaled nonlocal perimeters and of their first variations.

Abstract. We introduce a class of integral functionals known as nonlocal perimeters, which can be thought as interactions between a set and its complement that are weighted by a positive kernel. In the first part of the talk, we summarise the main features of these functionals and then we study the asymptotic behaviour of the family associated with mass-preserving rescalings of a given kernel. Namely, we prove that when the scaling parameter approaches $0$, the rescaled non local perimeters $Gamma$-converge to De Giorgi's perimeter, up to a multiplicative
Data Seminario: 
Wednesday, March 28, 2018
Relatore: 
Valerio Pagliari
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Uniqueness of solutions to singular Liouville equations

Relatore: 
Aleks Jevnikar
Abstract. We deduce new uniqueness results for solutions to singular Liouville equations both on spheres and on bounded domains, as well as a new self-contained proof of previously known results. To this end, we derive a singular Sphere Covering Inequality based on the Alexandrov-Bol isoperimetric inequality and symmetric rearrangements. Joint project with D. Bartolucci, C. Gui and A. Moradifam.
Data Seminario: 
Wednesday, March 21, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Duality for the W_\infty Wasserstein distance

Relatore: 
Luigi De Pascale
Abstract. I will first give a short survey to recall the importance of convexity in the classical Monge problem. I will then introduce the $W_\infty$ Wasserstein distance and discuss the lack of convexity of the underlying problem. The next step will be to present the dual problem introduced in 2016 by Barron, Bocea and Jensen. The maximum value of this dual problem coincides with the minimum value of the transport problem but it is not clear that non trivial maximizers exist.
Data Seminario: 
Wednesday, March 7, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Firenze
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

A Phase Field Model for Thin Elastic Structures with Topological Constraint

Relatore: 
Patrick Dondl
Abstract. With applications in the area of biological membranes in mind, we consider the problem of minimizing Willmore’s energy among the class of closed, connected surfaces with given surface area that are confined to a fixed container. Based on a phase field model for Willmore’s energy originally introduced by de Giorgi, we develop a technique to incorporate the connectedness constraint into a diffuse interface model of elastic membranes.
Data Seminario: 
Wednesday, March 14, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Freiburg
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Un approccio variazionale alla regolarità delle frontiere libere singolari

Abstract. In questo seminario affronteremo il problema della regolarità delle frontiere libere associate ai minimi del funzionale di Bernoulli. In un celebre lavoro degli anni ottanta, Alt e Caffarelli dimostrarono che le frontiere libere di Bernoulli si possono decomporre in due insiemi disgiunti: l'insieme dei punti piatti (Reg), localmente dato dal grafico di una funzione liscia, e l'insieme dei punti singolari (Sing), di dimensione di Hausdorff al massimo d-5.
Data Seminario: 
Wednesday, February 7, 2018
Relatore: 
Bozhidar Velichkov
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Stability of type II blow up solutions for critical wave equations

Abstract. I will discuss recent work on $\Box\, u=-u^5$, jointly with S. Burzio (EPFL), as well as ongoing work on co-rotational Wave Maps, jointly with S. Miao (EPFL).
Data Seminario: 
Wednesday, January 31, 2018
Relatore: 
Joachim Krieger
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Aula Magna (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

On the scaling limit of Onsager's molecular model for liquid crystals

Relatore: 
Yuning Liu
Abstract. We study the small Deborah number limit of the Doi-Onsager equation for the dynamics of nematic liquid crystals. This is a Smoluchowski-type equation that characterizes the evolution of a number density function, depending upon both particle position and its orientation vector, which lies on the unit sphere.
Data Seminario: 
Wednesday, January 17, 2018
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:15
Affiliazione: 
NYU University at Shanghai
Ora Inizio: 
Saturday, January 1, 0000 - 17:15

Willmore Flow of Networks

Abstract. We consider networks of curves in the plane moving according to the L^2-gradient flow of a variant of the elastic energy. In this talk we will prove short time existence in the case of networks composed by three curves that are required to meet in one or two triple junctions. As a variation of the result we additionally impose that they form an angle of 120 degrees at the triple junction(s). If time allows we will give some outlook on our expectations concerning the long time behaviour based on numerical work by John Barrett, Harald Garcke and Robert Nürnberg.
Data Seminario: 
Wednesday, November 29, 2017
Relatore: 
Julia Menzel
Ora Fine: 
Saturday, January 1, 0000 - 19:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 18:00

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