F. Cagnetti, M. G. Mora, M. Morini:
A second order minimality condition for the Mumford-Shah functional
Calc. Var. Vol. 33, p. 37-74, 2008

F. Cagnetti:
A vanishing viscosity approach to fracture growth in a cohesive zone model with prescribed crack path
Math. Models Methods Appl. Sci. Vol. 18/7, p. 1027-1071, 2008

F. Cagnetti:
k-Quasiconvexity Reduces to Quasiconvexity
Proc. Roy. Soc. Edinburgh Sect. A Vol. 141, p. 673-708, 2011

F. Cagnetti, D. Gomes, H. V. Tran:
Aubry-Mather Measures in the Non Convex setting
SIAM J. Math. Anal. Vol. 43, p. 2601-2629, 2011

F. Cagnetti, L. Scardia:
An extension theorem in $SBV$ and an application to the homogenization of the Mumford-Shah functional in perforated domains
J. Math. Pures Appl. Vol. 95, p. 349-381, 2011

F. Cagnetti, R. Toader:
Quasistatic crack evolution for a cohesive zone model  with different response to loading and unloading: a Young measures approach
ESAIM Control Optim. Calc. Var. Vol. 17, p. 1--27, 2011

F. Cagnetti, D. Gomes, H. Mitake, H. V. Tran:
A new method for large time behavior of degenerate viscous Hamilton-Jacobi equations  with convex Hamiltonians
Ann. Inst. H. Poincaré Anal. Non Linéaire (Accepted Paper) 2012

M. Barchiesi, F. Cagnetti, N. Fusco:
Stability of the Steiner symmetrization of convex sets
J. Eur. Math. Soc. Vol. 15, p. 1245-1278, 2013

F. Cagnetti, D. Gomes, H. V. Tran:
Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method
Appl. Numer. Math. Vol. 73, p. 2-15, 2013

F. Cagnetti, D. Gomes, H. V. Tran:
Adjoint Methods for Obstacle Problems and Weakly Coupled Systems of PDE
ESAIM Control Optim. Calc. Var. Vol. 19, p. 754-779, 2013

F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Rigidity of equality cases in Steiner's perimeter inequality
Anal. PDE (Accepted Paper) 2013

F. Cagnetti, M. Colombo, G. De Philippis, F. Maggi:
Essential connectedness and the rigidity problem for Gaussian
  symmetrization
J. Eur. Math. Soc. (Accepted Paper) 2013

M. Artina, F. Cagnetti, M. Fornasier, F. Solombrino:
Linearly Constrained Evolutions of Critical Points and an Application to Cohesive Fractures
Mathematical Models and Methods in Applied Sciences  Vol. 27, N. 02, p. 231-290, 2017

F. Cagnetti, G. Dal Maso, L. Scardia, C. I. Zeppieri:
$\Gamma$-convergence of free-discontinuity problems
Ann. Inst. H. Poincaré Anal. Non Linéaire 2018

F. Cagnetti:
Rigidity for Perimeter Inequalities under symmetrization:  state of the art and open problems
Portugaliae Mathematica (Accepted Paper) 2019

F. Cagnetti, M. Perugini, D. Stöger:
Rigidity for perimeter inequality under spherical symmetrisation
Calc. Var. Partial Differential Equations 2019

F. Cagnetti, G. Dal Maso, L. Scardia, C. I. Zeppieri:
Stochastic Homogenisation of Free-Discontinuity Problems
Arch. Ration. Mech. Anal. Vol. 233, p. 935-974, 2019

F. Cagnetti, A. Chambolle, L. Scardia:
Korn and Poincaré-Korn inequalities for functions with small jump set
Math. Ann. (Accepted Paper) 2020

L. Caffarelli, F. Cagnetti, A. Figalli:
Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive zone models
Arch. Ration. Mech. Anal. 2020

F. Cagnetti, A. Chambolle, M. Perugini, L. Scardia:
An extension result for generalised special functions  of bounded deformation
J. Convex Anal. 2021

F. Cagnetti, G. Dal Maso, L. Scardia, C. I. Zeppieri:
A global method for deterministic and stochastic homogenisation in BV
Ann. PDE Vol. 8, N. 1, p. Paper No. 8, 2022