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———

CVGMT preprint server  
Department of Mathematics, University of Pisa  
Centro di ricerca matematica E. De Giorgi, Pisa 

I have been working in the following areas: Real Analysis, Geometric Measure Theory and Calculus of Variations, with applications to partial differential equations and mathematical physics (phase separation, pattern formation, capillarity, Ginzburg-Landau vortices).

cv in english     cv in italian

I am currently involved in the following research projects:

Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni [Optimal transport, functional and geometric inequalities, and applications], PRIN project directed by Luigi Ambrosio (Scuola Normale Superiore, Pisa, Italy)

Hyperbolic systems of conservation laws: singular limits, properties of solutions and control problems, funded by an ERC starting grant awarded to Stefano Bianchini (SISSA, Trieste, Italy)

Local structure of sets, measures and currents, funded by an ERC advanced grant awarded to David Preiss (University of Warwick, UK)

On the L^p-differentiability of certain classes of functions
with Stefano Bianchini and Gianluca Crippa 
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

A uniqueness result for the continuity equation in two dimensions 
with Stefano Bianchini and Gianluca Crippa
to appear on J. Eur. Math. Soc. (JEMS)
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Structure of level sets and Sard-type properties of Lipschitz maps 
with Stefano Bianchini and Gianluca Crippa
to appear on Ann. Scuola Norm. Sup. Pisa Cl. Sci.
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Warning
The version of each papers stored in this page is as close as possible to the published one, but may be not exactly the same. If the published version is substantially shorter than the preprint, the latter is also available (suffix 'extended'). Most papers are also available in a reduced, paper-saving format (two pages per side, suffix 'rdc').
All downloadable files are PDF. 

Quasistatic evolution of sessile drops and contact angle hysteresis 
with Antonio DeSimone 
Arch. Rational Mech. Anal., 202 (2011), no. 1, 295-348
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Uniform energy distribution for an isoperimetric problem with long-range interactions 
with Rustum Choksi and Felix Otto
J. Amer. Math. Soc., 22 (2009), no. 2, 569-605
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Variational convergence for functionals of Ginzburg-Landau type
with Sisto Baldo and Giandomenico Orlandi
Indiana Univ. Math. J. 54 (2005), no. 5, 1411-1472
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

BV has the bounded approximation property
with Marianna Csörnyei, Aleksander Pełczyński and David Preiss
J. Geom. Anal.  15 (2005), no. 1, 1-7
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Wetting of rough surfaces: a homogenization approach
with Antonio DeSimone
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), no. 2053, 79-97
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

Functions with prescribed singularities
with Sisto Baldo and Giandomenico Orlandi
J. Eur. Math. Soc. (JEMS) 5 (2003), no. 3, 275-311
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

The calibration method for the Mumford-Shah functional and free discontinuity problems
with Guy Bouchitté and Gianni Dal Maso
Calc. Var. Partial Differential Equations, 16 (2003), no. 3, 299-333
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI  -  extended.pdf  -  extended-rdc.pdf]

On a long standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property
with Luigi Ambrosio and Xavier Cabré
Acta Appl. Math., 65 (2001), no. 1-3, 9-33
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

A new approach to variational problems with multiple scales
with Stefan Müller
Comm. Pure Appl. Math., 54 (2001), no. 7, 761-825
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

The calibration method for the Mumford-Shah functional
with Guy Bouchitté and Gianni Dal Maso
C. R. Acad. Sci. Paris, Sér. I Math., 329 (1999), no. 3, 249-254
[abstract.txt  -  full paper.pdf  -  MathSciNet  -  DOI]

Phase transition with line-tension effect
with Guy Bouchitté and Pierre Seppecher
Arch. Rational Mech. Anal., 144 (1998), no. 1, 1-46
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI]

A nonlocal anisotropic model for phase transitions: asymptotic behaviour of rescaled energies
with Giovanni Bellettini
European J. Appl. Math., 9 (1998), no. 3, 261-284
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI  -  extended.pdf  -  extended-rdc.pdf]

Rank one property for derivatives of functions with bounded variation
Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), no. 2, 239-274
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

A Lusin type theorem for gradients
J. Funct. Anal., 100 (1991), no. 1, 110-119
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet  -  DOI] 

Differentiability of Lipschitz functions, structure of null sets, and other problems
with Marianna Csörnyei and David Preiss (lecture delivered by M. Csörnyei)
in "Proceedings of the international congress of mathematicians (ICM 2010), Hyderabad, India, August 19-27, 2010". Volume 3 (invited lectures), pp. 1379-1394.
Edited by R. Bhatia et al. World Scientific, Hackensack (NJ) 2010
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

Geometric measure theory
in the "Encyclopedia of mathematical physics", vol. 2, pp. 520-527. Edited by J.-P. Françoise, G.L. Naber, S.T. Tsou. Academic Press/Elsevier Science, Oxford 2006
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

Distributional Jacobian and singularities of Sobolev maps
Ricerche Mat., 54 (2005), no. 2, 375-394
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

Structure of null sets in the plane and applications
with Marianna Csörnyei and David Preiss (lecture delivered by G. Alberti)
in "European Congress of Mathematics. Proceedings of the 4th Congress (4ECM) held in Stockholm,
June 27-July 2, 2004", pp. 3-22. Edited by A. Laptev. European Mathematical Society (EMS), Zürich 2005
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

Un risultato di convergenza variazionale per funzionali di tipo Ginzburg-Landau in dimensione qualunque
Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 4 (2001), no. 2, 289-310
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

A variational convergence result for functionals of Ginzburg-Landau type in any dimension
english translation of the previous paper (unpublished)
[full paper.pdf  -  full paper-rdc.pdf]

Variational models for phase transitions, an approach via Gamma-convergence
in L. Ambrosio, N. Dancer: "Calculus of variations and partial differential equations. Topics on geometrical evolution problems and degree theory. Papers from the Summer School held in Pisa, September 1996", pp. 95-114. Edited by G. Buttazzo, A. Marino, M.K.V. Murthy. Springer-Verlag, Berlin, 2000
[abstract.txt  -  full paper.pdf  -  full paper-rdc.pdf  -  MathSciNet]

Quasistatic evolution and contact-angle hysteresis in capillarity
course in the "ITN-Winterschool on Mathematical Models for Wetting: Analysis and Numerics".
Veilbronn (near Erlangen), February 13-17, 2012.
[abstract.txt  -  lect1.pdf (4.5 Mb)  -  lect2.pdf (5.7 Mb)  -  lect3.pdf (5.1 Mb)  -  lect4.pdf (5.5 Mb)]

Classical and non-classical tools for minimal surfaces
course in the "Fifth Summer School in Analysis and Applied Mathematics".
Roma, June 1-5, 2009.
[abstract.txt  -  lect1.pdf (1.8 Mb)  -  lect2.pdf (2.1 Mb)  -  lect3.pdf (2.1 Mb)  -  lect4.pdf (1.4 Mb)]

Sulla struttura degli insiemi di misura nulla. Applicazioni e problemi aperti
plenary lecture at the "XVIII congresso dell'Unione Matematica Italiana"
Bari, 24-29 settembre 2007.
[abstract.txt  -  complete presentation.pdf (1.9 Mb)]

Structure of null sets in the Euclidean space. Some results and open problems.
lecture at the conference "Real Analysis, Geometric Measure Theory, PDE and Banach Spaces". University of Warwick, August 17-19, 2007.
[abstract.txt  -  complete presentation.pdf (2.3 Mb)]

On maps whose distributional Jacobian is a measure.
lecture at the "Summer Symposium in Real Analysis XXXI".
Trinity College, Oxford, August 12-16, 2007.
[abstract.txt  -  complete presentation.pdf (1.9 Mb)]

Some applications of geometric measure theory
course in the school: "Geometric Measure Theory: Old and New".
Les Diablerets, April 3-8, 2005.
[abstract.txt  -  complete presentation.pdf (2.8 Mb)]