M. Focardi:
Semicontinuity of vectorial functionals in Orlicz-Sobolev spaces
Rend. Istit. Mat. Univ. Trieste  Vol. XXIX, p. 141-161, 1997

M. Focardi:
On the Variational Approximation of Free-Discontinuity Problems in the Vectorial Case
Math. Models Methods Appl. Sci. N. 11, p. 663-684, 2001

M. Focardi, E. Mascolo:
Lower semicontinuity for quasiconvex functionals with non standard growth
Journal of Convex Analysis Vol. 8, p. 1-22, 2001

R. Alicandro, M. Focardi, M. S. Gelli:
Finite-Difference Approximation of Energies in Fracture Mechanics
Ann. Scuola Norm. Sup. Pisa Cl. Sci. Vol. 4, N. 29, p. 671-709, 2001

M. Focardi:
Variational Approximation of Vectorial Free Discontinuity Problems: the Discrete and Continuous Case
(Ph.D. Thesis) 2002

B. Bianconi, M. Focardi, E. Mascolo:
Existence of minimizers for a class of quasiconvex functionals with non standard growth
Ann. Matematica Pura e Applicata Vol. 4, N. 180, p. 493-510, 2002

R. Alicandro, M. Focardi:
Variational Approximation of Free-Discontinuity Energies with Linear Growth
Comm. Cont. Math. Vol. 4, N. 4, p. 685-723, 2002

M. Focardi, M. S. Gelli:
Approximation results by difference schemes of Fracture Energies: the vectorial case.
NoDEA Vol. 10, N. 4, p. 469-495, 2003

M. Focardi, P. M. Mariano:
Convergence of asynchronous variational integrators in linear elastodynamics
Int. J. Numer. Meth. Engng. 2007

M. Focardi, A. Garroni:
A $1$D phase field model for dislocations and a second order $\Gamma$limit
SIAM Multiscale Model. Simul. Vol. 6, N. 4, p. 1098-1124, 2007

M. Focardi, M. S. Gelli:
Asymptotic analysis of Mumford-Shah type energies in periodically perforated domains
Inter. Free Boundaries Vol. 9, p. 107-132, 2007

M. Focardi, M. S. Gelli:
Relaxation of free-discontinuity energies with obstacle
ESAIM COCV Vol. 14, N. 4, p. 879--896, 2008

M. Focardi, M. S. Gelli, M. Ponsiglione:
Fracture mechanics in perforated domains: a variational model for brittle porous media
Math. Models Methods Appl. Sci.  Vol. 19, N. 11, p. 2065-2100, 2009

M. Focardi:
Homogenization of fractional obstacle problems via $\Gamma$-convergence
Comm. Partial Differential Equations Vol. 34, p. 1607-1631, 2009

M. Focardi, P. M. Mariano:
Discrete dynamics of complex bodies with substructural dissipation: variational integrators and  convergence
Discrete Contin. Dynam. Systems B Vol. 11, N. 1, p. 109-130, 2009

M. Focardi:
Aperiodic fractional obstacle problems
Advances in Mathematics Vol. 225, p. 36, 2010

M. Focardi, M. S. Gelli, G. Pisante:
On a 1-capacitary type problem in the plane
Commun. Pure Appl. Anal. Vol. 9, N. 5, p. 1319-1333, 2010

C. De Lellis, M. Focardi, E. Spadaro:
Lower semicontinuous functionals for Almgren's multiple valued functions
Annales Academiae Scientiarum Fennicae Mathematica Vol. 36, p. 1-18, 2011

M. Barchiesi, M. Focardi:
Homogenization of the Neumann problem in perforated domains: an alternative approach
Calc. Var. Partial Differential Equations Vol. 42, p. 257-288 , 2011

M. Focardi:
Vector-valued obstacle problems for non-local energies
Discr. Contin. Dyn. Syst. B Vol. 17, p. 487-507, 2012

M. Focardi:
$\Gamma$-convergence: a tool to investigate physical phenomena across scales 
Mathematical Models and Methods in Applied Sciences Vol. 35, N. 14, p. 1613-1658, 2012

M. Focardi:
Regularity issues for local minimizers of the Mumford &  Shah energy in 2d
Bruno Pini Mathematical Analysis Seminar () p. 14--32, 2012

M. Focardi, E. Spadaro:
An intrinsic approach to manifold constrained variational problems
Annali di Matematica Pura e Applicata Vol. 192, p. 145-163, 2013

C. De Lellis, M. Focardi:
Higher integrability of the gradient for minimizers of the 2d Mumford-Shah energy 
J. Math. Pures Appl. Vol. 100, p. 391-409, 2013

C. De Lellis, M. Focardi:
Density lower bound estimates for local minimizers of the 2d Mumford-Shah energy
Manuscripta Math. Vol. 132, p. 215-232, 2013

M. Focardi, P. M. Mariano, E. Spadaro:
 Multi-value microstructural descriptors for finer scale material  complexity: analysis of ground states
Archive for Rational Mechanics and Analysis (Accepted Paper) 2013

M. Focardi, P. Marcellini:
On The Lower Semicontinuity Of Quasiconvex Integrals 
Bulletin of the Institute of Mathematics Academia Sinica Vol. 9, N. 2, p. 245--266, 2014

M. Focardi, N. Fusco, C. Leone, P. Marcellini, E. Mascolo, A. Verde:
Weak lower semicontinuity for polyconvex integrals in the limit case
Calc. Var. Partial Differential Equations Vol. 51, N. 1-2, p. 171-193, 2014

M. Focardi, F. Iurlano:
Asymptotic analysis of Ambrosio-Tortorelli energies in linearized elasticity
SIAM Journal on Mathematical Analysis Vol. 46, p. 2936--2955, 2014

C. De Lellis, M. Focardi, B. Ruffini:
A note on the Hausdorff dimension of the singular set for minimizers of the Mumford-Shah energy
Adv. Calc. Var. Vol. 7, N. 4, p. 539-545, 2014

M. Focardi, M. S. Gelli, E. Spadaro:
Monotonicity formulas for obstacle problems with Lipschitz coefficients
Calc. Var. Partial Differential Equations 2015

M. Focardi, A. Marchese, E. Spadaro:
Improved estimate of the singular set of Dir-minimizing Q-valued functions via an abstract regularity result
Journal of Functional Analysis Vol. 268, p. 3290--3325, 2015

M. Focardi, F. Geraci, E. Spadaro:
The classical obstacle problem for nonlinear variational energies
(Nonlinear Analysis TMA) 2016

S. Conti, M. Focardi, F. Iurlano:
Integral representation for functionals defined on $SBD^p$ in dimension two
(Archive for Rational Mechanics and Analysis) 2016

M. Focardi:
Fine regularity results  for Mumford-Shah minimizers: porosity, higher integrability and the Mumford-Shah conjecture
(CRM series 19) 2016

S. Conti, M. Focardi, F. Iurlano:
Which special functions of bounded deformation have bounded variation?
Proc. Roy. Soc. Edinburgh Sect. A Vol. 148A, p. 33--50, 2016

S. Conti, M. Focardi, F. Iurlano:
Existence of minimizers for the $2$d stationary Griffith fracture model
C. R. Acad. Sci. Paris, Ser. I Vol. 354, N. 11, p. 1055--1059, 2016

M. Focardi, E. Spadaro:
An epiperimetric inequality for the thin obstacle problem
Advances in Differential Equations Vol. 21, N. 1-2, p. 153--200, 2016

G. De Philippis, S. Di Marino, M. Focardi:
Lower semicontinuity for  non-coercive polyconvex integrals in the limit case
Proceedings of the Royal Society of Edinburgh Vol. 146A, p. 243--264, 2016

S. Conti, M. Focardi, F. Iurlano:
Phase field approximation of cohesive fracture models
Ann. I. H. Poincaré Vol. 33, p. 1033--1067, 2016

S. Conti, M. Focardi, F. Iurlano:
Approximation of fracture energies with $p$-growth via piecewise affine finite elements
ESAIM COCV (Accepted Paper) 2017

M. Focardi, F. Geraci, E. Spadaro:
Quasi-monotonicity formulas for classical obstacle problems with Sobolev coefficients and applications
JOTA 2018

M. Focardi, E. Spadaro:
On the measure and the structure of the free boundary  of the lower dimensional obstacle problem
Archive for Rational Mechanics and Analysis Vol. 230, p. 125--184, 2018

S. Conti, M. Focardi, F. Iurlano:
Existence of strong minimizers for the Griffith static fracture model in dimension two
Ann. I. H. Poincaré 2018

S. Conti, M. Focardi, F. Iurlano:
A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems
Commun. Contemp. Math. 2018

M. Focardi, E. Spadaro:
The local structure of the free boundary in the fractional obstacle problem
Advances in Calculus of Variations (Accepted Paper) 2019

G. Cupini, M. Focardi, F. Leonetti, E. Mascolo:
On the H\"older continuity for a class of vectorial problems
Adv. Nonlinear Anal. Vol. 9, p. 1008-1025, 2020

M. Caroccia, M. Focardi, N. Van Goethem:
On the integral representation of variational functionals on $BD$
SIAM J. Math. Anal. Vol. 52, N. 4, p. 40224067, 2020

M. Focardi, E. Spadaro:
How a minimal surface leaves a thin obstacle
Annales de l'Institut Henri Poincaré C, Analyse non linéaire Vol. 37, N. 4, p. 1017-1046, 2020

C. De Lellis, M. Focardi, S. Ghinassi:
Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan
J. Math. Pures Appl. (Accepted Paper) 2020

M. Cicalese, M. Focardi, C. I. Zeppieri:
Phase-field approximation of functionals defined on piecewise-rigid maps
J. Nonlinear Sci. Vol. 31, N. 5, p. Paper No. 78, 25pp, 2021

S. Conti, M. Focardi, F. Iurlano:
Phase-field approximation of  a  vectorial, geometrically nonlinear cohesive fracture energy
(Preprint) 2022

G. Andreucci , M. Focardi:
The classical obstacle problem with H\"older continuous coefficients
Nonlinear Anal. Vol. 226, 2023

C. De Lellis, M. Focardi:
The regularity theory for the Mumford-Shah functional on the plane
(Lecture Notes) 2023

S. Conti, M. Focardi, F. Iurlano:
Approximation of $SBV$ functions with possibly infinite jump set
(Submitted Paper) 2023