cvgmt: Matteo Focardi

Calculus of Variations and Geometric Measure Theory

Matteo Focardi

[focardi]

Full Professor, Università di Firenze

Email: matteo.focardi AT unifi.it

Home-page: https://people.dimai.unifi.it/focardi/

orcid id: 0000-0001-5278-7747

Available papers (66):

F. Deangelis - M. Focardi - C. I. Zeppieri (Submitted Paper)
Stochastic homogenization of fractional obstacle problems (2026)
M. Focardi (Preprint)
The Bourgain, Brezis, Mironescu localization for deterministic obstacle problems (2026)
F. Deangelis - C. De Lellis - M. Focardi (Preprint)
A remark on the global minimality of the cracktip (2026)
F. Colasanto - M. Focardi - M. Fornasier - F. Mattesini (preprint)
Sharp Rates of MMD Empirical Estimation with Power Kernels (2026)
M. Focardi - G. Palatucci - C. I. Zeppieri (Preprint)
Fractional capacitary potentials: Wolff and Riesz representations, far-field decay, and removability (2026)
S. Conti - M. Focardi - F. Iurlano (Calculus of Variations and Partial Differential Equations)
Superlinear free-discontinuity models: relaxation and phase field approximation (2026)
R. Alessi - F. Colasanto - M. Focardi (SIAM Journal on Mathematical Analysis)
Phase-field modelling of cohesive fracture. Part I: $\Gamma$-convergence results (2026)
G. Andreucci - M. Focardi - E. Spadaro (Interfaces and Free Boundaries)
On the free boundary for thin obstacle problems with Sobolev variable coefficients (2026)
R. Alessi - F. Colasanto - M. Focardi (International Journal of Solids and Structures)
Phase-field modelling of cohesive fracture. Part III: From mathematical results to engineering applications (2026)
R. Alessi - F. Colasanto - M. Focardi (Preprint)
Phase-field modelling of cohesive fracture. Part II: Reconstruction of the cohesive law (2025)
C. De Lellis - M. Focardi (Lecture Notes: EMS Monographs in Mathematics)
The regularity theory for the Mumford-Shah functional on the plane (2025)
F. Colasanto - M. Focardi - C. I. Zeppieri (Accepted Paper: Calc. Var. Partial Differential Equations)
Homogenisation of phase-field functionals with linear growth (2025)
S. Conti - M. Focardi - F. Iurlano (JOURNAL OF FUNCTIONAL ANALYSIS)
Approximation of $SBV$ functions with possibly infinite jump set (2025)
G. Andreucci - M. Focardi (Nonlinear Anal.)
The classical obstacle problem with H\"older continuous coefficients (2023)
S. Conti - M. Focardi - F. Iurlano (Archive for Rational Mechanics and Analysis)
Phase-field approximation of a vectorial, geometrically nonlinear cohesive fracture energy (2022)
M. Cicalese - M. Focardi - C. I. Zeppieri (J. Nonlinear Sci.)
Phase-field approximation of functionals defined on piecewise-rigid maps (2021)
G. Cupini - M. Focardi - F. Leonetti - E. Mascolo (Adv. Nonlinear Anal.)
On the H\"older continuity for a class of vectorial problems (2020)
M. Caroccia - M. Focardi - N. Van Goethem (SIAM J. Math. Anal.)
On the integral representation of variational functionals on $BD$ (2020)
M. Focardi - E. Spadaro (Annales de l'Institut Henri Poincaré C, Analyse non linéaire)
How a minimal surface leaves a thin obstacle (2020)
C. De Lellis - M. Focardi - S. Ghinassi (J. Math. Pures Appl.)
Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan (2020)
M. Focardi - E. Spadaro (Advances in Calculus of Variations)
The local structure of the free boundary in the fractional obstacle problem (2019)
M. Focardi - F. Geraci - E. Spadaro (JOTA)
Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications (2018)
M. Focardi - E. Spadaro (Archive for Rational Mechanics and Analysis)
On the measure and the structure of the free boundary of the lower dimensional obstacle problem (2018)
S. Conti - M. Focardi - F. Iurlano (Ann. I. H. Poincaré)
Existence of strong minimizers for the Griffith static fracture model in dimension two (2018)
S. Conti - M. Focardi - F. Iurlano (Commun. Contemp. Math.)
A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems (2018)
S. Conti - M. Focardi - F. Iurlano (Accepted Paper: ESAIM COCV)
Approximation of fracture energies with $p$-growth via piecewise affine finite elements (2017)
M. Focardi - F. Geraci - E. Spadaro (Nonlinear Analysis TMA)
The classical obstacle problem for nonlinear variational energies (2016)
S. Conti - M. Focardi - F. Iurlano (Archive for Rational Mechanics and Analysis)
Integral representation for functionals defined on $SBD^p$ in dimension two (2016)
M. Focardi (CRM series 19)
Fine regularity results for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture (2016)
S. Conti - M. Focardi - F. Iurlano (Proc. Roy. Soc. Edinburgh Sect. A)
Which special functions of bounded deformation have bounded variation? (2016)
S. Conti - M. Focardi - F. Iurlano (C. R. Acad. Sci. Paris, Ser. I)
Existence of minimizers for the $2$d stationary Griffith fracture model (2016)
M. Focardi - E. Spadaro (Advances in Differential Equations)
An epiperimetric inequality for the thin obstacle problem (2016)
G. De Philippis - S. Di Marino - M. Focardi (Proceedings of the Royal Society of Edinburgh)
Lower semicontinuity for non-coercive polyconvex integrals in the limit case (2016)
S. Conti - M. Focardi - F. Iurlano (Ann. I. H. Poincaré)
Phase field approximation of cohesive fracture models (2016)
M. Focardi - M. S. Gelli - E. Spadaro (Calc. Var. Partial Differential Equations)
Monotonicity formulas for obstacle problems with Lipschitz coefficients (2015)
M. Focardi - A. Marchese - E. Spadaro (Journal of Functional Analysis)
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result (2015)
M. Focardi - P. Marcellini (Bulletin of the Institute of Mathematics Academia Sinica)
On The Lower Semicontinuity Of Quasiconvex Integrals (2014)
M. Focardi - F. Iurlano (SIAM Journal on Mathematical Analysis)
Asymptotic analysis of Ambrosio-Tortorelli energies in linearized elasticity (2014)
M. Focardi - N. Fusco - C. Leone - P. Marcellini - E. Mascolo - A. Verde (Calc. Var. Partial Differential Equations)
Weak lower semicontinuity for polyconvex integrals in the limit case (2014)
C. De Lellis - M. Focardi - B. Ruffini (Adv. Calc. Var.)
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy (2014)
M. Focardi - E. Spadaro (Annali di Matematica Pura e Applicata)
An intrinsic approach to manifold constrained variational problems (2013)
C. De Lellis - M. Focardi (J. Math. Pures Appl.)
Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energy (2013)
C. De Lellis - M. Focardi (Manuscripta Math.)
Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy (2013)
M. Focardi - P. M. Mariano - E. Spadaro (Accepted Paper: Archive for Rational Mechanics and Analysis)
Multi-value microstructural descriptors for finer scale material complexity: analysis of ground states (2013)
M. Focardi (Discr. Contin. Dyn. Syst. B)
Vector-valued obstacle problems for non-local energies (2012)
M. Focardi (Mathematical Models and Methods in Applied Sciences)
$\Gamma$-convergence: a tool to investigate physical phenomena across scales (2012)
M. Focardi (Bruno Pini Mathematical Analysis Seminar)
Regularity issues for local minimizers of the Mumford & Shah energy in 2d (2012)
C. De Lellis - M. Focardi - E. Spadaro (Annales Academiae Scientiarum Fennicae Mathematica)
Lower semicontinuous functionals for Almgren's multiple valued functions (2011)
M. Barchiesi - M. Focardi (Calc. Var. Partial Differential Equations)
Homogenization of the Neumann problem in perforated domains: an alternative approach (2011)
M. Focardi (Advances in Mathematics)
Aperiodic fractional obstacle problems (2010)
M. Focardi - M. S. Gelli - G. Pisante (Commun. Pure Appl. Anal.)
On a 1-capacitary type problem in the plane (2010)
M. Focardi - M. S. Gelli - M. Ponsiglione (Math. Models Methods Appl. Sci. )
Fracture mechanics in perforated domains: a variational model for brittle porous media (2009)
M. Focardi (Comm. Partial Differential Equations)
Homogenization of fractional obstacle problems via $\Gamma$-convergence (2009)
M. Focardi - P. M. Mariano (Discrete Contin. Dynam. Systems B)
Discrete dynamics of complex bodies with substructural dissipation: variational integrators and convergence (2009)
M. Focardi - M. S. Gelli (ESAIM COCV)
Relaxation of free-discontinuity energies with obstacle (2008)
M. Focardi - P. M. Mariano (Int. J. Numer. Meth. Engng.)
Convergence of asynchronous variational integrators in linear elastodynamics (2007)
M. Focardi - A. Garroni (SIAM Multiscale Model. Simul.)
A $1$D phase field model for dislocations and a second order $\Gamma$limit (2007)
M. Focardi - M. S. Gelli (Inter. Free Boundaries)
Asymptotic analysis of Mumford-Shah type energies in periodically perforated domains (2007)
M. Focardi - M. S. Gelli (NoDEA)
Approximation results by difference schemes of Fracture Energies: the vectorial case. (2003)
M. Focardi (Ph.D. Thesis)
Variational Approximation of Vectorial Free Discontinuity Problems: the Discrete and Continuous Case (2002)
B. Bianconi - M. Focardi - E. Mascolo (Ann. Matematica Pura e Applicata)
Existence of minimizers for a class of quasiconvex functionals with non standard growth (2002)
R. Alicandro - M. Focardi (Comm. Cont. Math.)
Variational Approximation of Free-Discontinuity Energies with Linear Growth (2002)
M. Focardi (Math. Models Methods Appl. Sci.)
On the Variational Approximation of Free-Discontinuity Problems in the Vectorial Case (2001)
M. Focardi - E. Mascolo (Journal of Convex Analysis)
Lower semicontinuity for quasiconvex functionals with non standard growth (2001)
R. Alicandro - M. Focardi - M. S. Gelli (Ann. Scuola Norm. Sup. Pisa Cl. Sci.)
Finite-Difference Approximation of Energies in Fracture Mechanics (2001)
M. Focardi (Rend. Istit. Mat. Univ. Trieste )
Semicontinuity of vectorial functionals in Orlicz-Sobolev spaces (1997)

Seminars:

30 oct 2020: On the regularity of singular sets of minimizers for the Mumford-Shah energy
11 sep 2018: The measure and the structure of the free boundary in the lower dimensional obstacle problem
7 jul 2014: Fine regularity results for Mumford-Shah minimizers: higher integrability of the gradient and estimates on the Hausdorff dimension of the singular set
9 may 2012: Regularity issues for local minimizers of the Mumford-Shah functional in 2D
17 feb 2000: Finite Difference Approximation of Energies in Fracture Mechanics

Speaker:

6 sep 2027 - 9 sep 2027: Calculus of Variations and Applied Analysis in Linz
20 jul 2026 - 23 jul 2026: Summer Workshop in the Calculus of Variations
14 jul 2026 - 17 jul 2026: New Challenges in Calculus of Variations
19 jan 2026 - 21 jan 2026: When CalcVar meets Siena
23 sep 2025 - 24 sep 2025: Workshop on free boundary and geometric variational problems in Naples
2 jun 2024 - 8 jun 2024: First Chinese-Italian Workshop on Elliptic PDEs and Variational Problems
29 may 2023 - 2 jun 2023: Geometric Measure Theory, Bressanone 2023
30 oct 2020 - 30 oct 2020: Incontri di Analisi Matematica tra Firenze, Pisa e Siena
10 oct 2018 - 12 oct 2018: Topics in Nonlinear Analysis: Calculus of Variations and PDEs
24 sep 2018 - 28 sep 2018: Workshop MAR: Metric Analysis and Regularity
16 nov 2017 - 17 nov 2017: Variational and Geometrical Methods For PDEs
14 sep 2017 - 15 sep 2017: Workshop "Calculus of Variations and Partial Differential Equations"
13 feb 2017 - 16 feb 2017: Miniworkshop on dislocations, plasticity, and fracture
11 jul 2016 - 15 jul 2016: THE TOTAL VARIATION FLOW AND RELATED NONLINEAR EVOLUTION PROBLEMS

Organizer:

1 feb 2027 - 5 feb 2027: XXXVI Convegno Nazionale di Calcolo delle Variazioni
27 nov 2026 - 27 nov 2026: An autumn day in Calculus of Variations & Applications
9 feb 2026 - 13 feb 2026: XXXV Convegno Nazionale di Calcolo delle Variazioni
16 may 2025 - 16 may 2025: Calculus of Variations & Applications in Florence
10 feb 2025 - 14 feb 2025: XXXIV Convegno Nazionale di Calcolo delle Variazioni
12 feb 2024 - 16 feb 2024: XXXIII Convegno Nazionale di Calcolo delle Variazioni
12 jun 2023 - 16 jun 2023: Calculus of Variations and Geometric Measure Theory
8 may 2023 - 12 may 2023: XXXII Convegno Nazionale di Calcolo delle Variazioni
13 jun 2022 - 17 jun 2022: Advances in Calculus of Variations
28 nov 2019 - 29 nov 2019: Two days on CalcVar&PDEs
2 sep 2019 - 6 sep 2019: CIME Course "Geometric Measure Theory and Applications: From Geometric Analysis to Free Boundary Problems"
8 nov 2018 - 9 nov 2018: Workshop on dynamical systems, calculus of variations and control