5 papers
A global method for deterministic and stochastic homogenisation in
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia +1
In this paper we study the deterministic and stochastic homogenisation of free-discontinuity functionals under \emph{linear} growth and coercivity conditions. The main novelty of o…
Rigidity for perimeter inequality under spherical symmetrisation
Filippo Cagnetti, Matteo Perugini, Dominik Stöger
Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogo…
Stochastic Homogenisation of Free-Discontinuity Problems
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia +1
In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence o…
Essential connectedness and the rigidity problem for Gaussian symmetrization
Filippo Cagnetti, Maria Colombo, Guido De Philippis +1
We provide a geometric characterization of rigidity of equality cases in Ehrhard's symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new…
A second order minimality condition for the Mumford-Shah functional
Filippo Cagnetti, Maria Giovanna Mora, Massimiliano Morini
A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal qua…