Welcome to the Home Page of the Research Group in Calculus of Variations and Geometric Measure Theory at Pisa. Look here to know more about us. Please, feel free to download and use all the material you find interesting. If you want to receive regularly the group news, subscribe to our mailing list in the mail section.

If you want to receive an account to insert your preprints, fill-in the account request.

- Geometric Measure Theory in non Euclidean spaces (Luigi Ambrosio) > papers
- Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture (Gianni Dal Maso)
- Analytic Techniques for Geometric and Functional Inequalities (Nicola Fusco)
- Analysis of Optimal Sets and Optimal Constants: Old Questions and New Results (Aldo Pratelli)
- Mathematics for Shape Memory Technologies in Biomechanics (Ulisse Stefanelli)
- Geometry of Metric Groups (Enrico Le Donne) > papers
- Variational approach to the regularity of the free boundaries (Bozhidar Velichkov)

- 3 Posizioni di Ricercatore TD Tipo B - Mat/05 - Dipartimento di Matematica dell'Univ. di Napoli Federico II (deadline: 29 Apr 2021)
- Call for expression of interest in positions (Tenure Track, Associate Professor, Full Professor) at the Mathematics Department (University of Pisa) (deadline: 30 Apr 2021)
- PhD position in spectral theory of differential operators, Oldenburg (deadline: 7 May 2021)
- 4 PhD Positions at Radboud University (deadline: 7 May 2021)
- Post doc position in Mathematical Analysis - 1+1 - Trento (deadline: 13 May 2021)
- PhD position on "mixing in magnetic fluids" at KIT (deadline: 14 May 2021)
- 2 Postdoc and 1 PhD positions in Vienna (deadline: 15 May 2021)
- Five PhD position at Roma Tor Vergata University (deadline: 17 May 2021)
- Women in STEM Dissertation Award – IV Edizione (deadline: 4 Jun 2021)
- Recruitment of Shing-Tung Yau Center of Southeast University (SEU-Yau Center) Nanjing, China (deadline: 11 Feb 2022)
- Recruitment of the Nanjing Center for Applied Mathematics（NCAM） Nanjing, China (deadline: 11 Feb 2022)

- 21 Apr 2021:
**R. L. Frank:***From the liquid drop model for nuclei to the ionization conjecture for atoms* - 22 Apr 2021:
**J. L. Vazquez:***The theory of fractional p-Laplacian equations* - 29 Apr 2021:
**J. Mass:***Homogenisation of discrete dynamical optimal transport* - 29 Apr 2021:
**M. Fathi:***A proof of the Caffarelli contraction theorem via entropic interpolation* - 5 May 2021:
**A. DeSimone:***Motilità biologica e robot bio-ispirati: nuove sfide e opportunità e per la matematica*

- 18 Nov 2020 - 15 Sep 2021: NCTS International Geometric Measure Theory Seminar
- 7 - 21 Apr 2021: Lecture Series "Slicing and fine properties of $BV^{\mathcal A}$ functions"
- 19 - 21 May 2021: ''Workshop on $L^\infty$ and constrained variational problems''. Online
- 7 - 11 Jun 2021: Workshop "Variational methods and applications" Centro De Giorgi, Pisa
- 21 - 25 Jun 2021: Tenth Summer School in Analysis and Applied Mathematics Dipartimento di Matematica - Sapienza, Università di Roma
- 28 Jun - 2 Jul 2021: Como Lake School Mathematical Models for Bio-Medical Sciences moved to 2021 Villa del Grumello, Como
- 5 - 9 Jul 2021: Special session "Sub-Riemannian Geometry and Interactions", within the AMS-SMF-EMS Joint International Meeting in Grenoble, 2021 Grenoble
- 9 - 20 Aug 2021: 30th Jyväskylä Summer School Jyväskylä, Finland
- 20 Sep - 17 Dec 2021: Distributed Solutions to Complex Societal Problems University of Chicago, USA
- 6 - 8 Apr 2022: Probability, Analysis and Dynamics '22 Bristol
- 13 - 17 Jun 2022: Shape Optimization, related topics and applications Roskoff Biological center, Bretagne
- 19 - 23 Sep 2022: Shape Optimisation and Geometric Spectral Theory ICMS, Edinburgh

- A. Rueland - A. Tribuzio (Submitted Paper)

On the Energy Scaling Behaviour of a Singularly Perturbed Tartar Square (2021) - Q. H. Nguyen - C. P. Nguyen (Accepted Paper:
*Analysis and PDEs*)

Existence and regularity estimates for quasilinear equations with measure data: the case $1(2021)

- Q. H. Nguyen (Accepted Paper:
*Memoris of the AMS*)

Potential estimates and quasilinear parabolic equations with measure data (2021) - M. Goldman - M. Novaga - B. Ruffini (Submitted Paper)

Reifenberg flatness for quasi-minimizers of the perimeter under minimal assumptions (2021) - P. Bonicatto - G. Del Nin - E. Pasqualetto (preprint)

Decomposition of integral metric currents (2021) - E. Davoli - A. Molchanova - U. Stefanelli (Submitted Paper)

Equilibria of charged hyperelastic solids (2021) - R. Frank - T. Koenig - H. Kovarik (Preprint)

Blow-up of solutions of critical elliptic equation in three dimensions (2021) - R. Frank - T. Koenig - H. Kovarik (
*Calc. Var. Partial Differential Equations*)

Energy asymptotics in the three-dimensional Brezis--Nirenberg problem (2021) - H. Kovarik - Y. Pinchover (
*Comm. Cont. Mathematics*)

On minimal decay at infinity of Hardy-weights (2020) - H. Kovarik - K. Pankrashkin (
*J. Differential Equations*)

Robin eigenvalues on domains with peaks (2019) - H. Kovarik - T. Weidl - B. Ruszkowski (
*J. Spectr. Theory*)

Melas-type bounds for the Heisenberg Laplacian on bounded domains (2018) - H. Kovarik - K. Pankrashkin (
*Calc. Var. Partial Differential Equations*)

On the p-Laplacian with Robin boundary conditions and boundary trace theorems (2017) - A. Carbotti (Ph.D. Thesis)

Approximation properties of solutions to fractional equations, Riemann-Liouville fractional Sobolev spaces and a variational problem in Carnot Groups. (2020) - E. Mukoseeva (Ph.D. Thesis)

Second variation techniques for stability in geometric inequalities (2020) - E. Marconi (Preprint)

Characterization of minimizers of Aviles-Giga functionals on special domains (2021) - I. Mondello - A. Mondino - R. Perales (Submitted Paper)

An upper bound on the revised first Betti number and a torus stability result for RCD spaces (2021) - K. Bołbotowski - G. Bouchitté (Preprint)

Optimal design versus maximal Monge-Kantorovich metrics (2021) - A. Figalli - X. Ros-Oton - J. Serra (Preprint)

The singular set in the Stefan problem (2021) - C. Mantegazza - M. Novaga - A. Pluda (Preprint)

Type-0 singularities in the network flow - Evolution of trees (2021) - E. Bruè - Q. Deng - D. Semola (Preprint)

Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces (2021) - M. Magnabosco - C. Rigoni - G. Sosa (Submitted Paper)

Convergence of metric measure spaces satisfying the CD condition for negative values of the dimension parameter (2021)

- J. F. Babadjian - G. A. Francfort (Accepted Paper:
*Comm. Pure Appl. Math.*)

Continuity equation and characteristic flow for scalar Hencky plasticity (2021) - F. Farroni (
*Ricerche di Matematica*)

Asymptotic stability estimates for some evolution problems with singular convection fiels (2020) - F. Farroni - S. Guarino Lo Bianco - R. Schiattarella (
*Journal of Mathematical Analysis and Applications*)

BMO-Type seminorms generating Sobolev functions (2020) - F. Farroni - N. Fusco - S. Guarino Lo Bianco - R. Schiattarella (
*J. Funct. Anal.*)

A formula for the anisotropic total variation of SBV functions (2019) - F. Farroni - L. Greco - G. Moscariello - G. Zecca (
*Calc. Var. and Partial Differential Equations*)

Noncoercive quasilinear elliptic operators with singular lower order terms (2021) - A. Bach - M. Ruf (Preprint)

Fluctuation estimates for the multi-cell formula in stochastic homogenization of partitions (2021) - E. Davoli - L. Scarpa - L. Trussardi (Accepted Paper:
*Journal of Differential Equations*)

Local asymptotics for nonlocal convective Cahn-Hilliard equations with $W^{1,1}$ kernel and singular potential (2021) - A. Agrachev - D. Barilari - E. Paoli (
*Annales de l'Institut Fourier*)

Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics (2019) - D. Barilari - Y. Chitour - F. Jean - D. Prandi - M. Sigalotti (
*Journal de Mathématiques Pures et Appliquées*)

On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures (2020) - D. Barilari - U. Boscain - R. W. Neel (
*Annales de la Faculté des Sciences de Toulouse*)

Heat kernel asymptotics on sub-Riemannian manifolds with symmetries and applications to the bi-Heisenberg group (2019) - D. Barilari - U. Boscain - G. Charlot - R. W. Neel (
*Int. Math. Res. Not.*)

On the heat diffusion for generic Riemannian and sub-Riemannian structures (2017) - D. Barilari - F. Boarotto (
*Journal of Evolution Equations*)

Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature (2018) - D. Barilari - S. Ivanov (
*Calc. Var. PDE*)

A Bonnet-Myers type theorem for quaternionic contact structures (2019) - S. Almi - M. Morandotti - F. Solombrino (Accepted Paper:
*Journal of Evolution Equations*)

A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games (2020) - N. De Ponti - A. Mondino - D. Semola (
*Journal of Functional Analysis*)

The equality case in Cheeger's and Buser's inequalities on $ \mathsf{RCD}$ spaces (2021) - K. Fässler - A. Pinamonti (Preprint)

Loomis-Whitney inequalities in Heisenberg groups (2021) - C. Maor - M. G. Mora (Accepted Paper:
*Journal of Nonlinear Science*)

Reference configurations vs. optimal rotations: a derivation of linear elasticity from finite elasticity for all traction forces (2021) - L. Brasco - G. De Philippis - G. Franzina (Accepted Paper:
*Comm. Partial Differential Equations*)

Positive solutions to the sublinear Lane-Emden equation are isolated (2021) - B. Bulanyi - A. Lemenant (Accepted Paper:
*ESAIM Control Optim. Calc. Var.*)

Regularity for the planar optimal $p$-compliance problem (2021) - B. Bulanyi (
*Journal of Mathematical Analysis and Applications*)

On the importance of the connectedness assumption in the statement of the optimal $p$-compliance problem (2021) - L. Ambrosio - D. Tewodrose - S. Honda - J. Portegies (
*Journal of Functional Analysis*)

Embedding of $RCD^*(K,N)$ spaces in $L^2$ via eigenfunctions (2021) - D. Tewodrose (Accepted Paper:
*Annales Academiæ Scientiarum Fennicæ Mathematica*)

Adimensional weighted Sobolev inequalities in PI spaces (2020)