3 papers
math.AP2025
Symmetry breaking for local minimizers of a free discontinuity problem
Massimo Gobbino, Nicola Picenni
We study a functional defined on the class of piecewise constant functions, combining a jump penalization, which discourages discontinuities, with a fidelity term that penalizes de…
math.AP2023
Multi-scale analysis of minimizers for a second order regularization of the Perona-Malik functional
Massimo Gobbino, Nicola Picenni
We investigate the asymptotic behavior of minimizers for the singularly perturbed Perona-Malik functional in one dimension. In a previous study, we have shown that blow-ups of thes…
math.FA2023
Gamma-liminf estimate for a class of non-local approximations of Sobolev and BV norms
Massimo Gobbino, Nicola Picenni
We consider a family of non-local and non-convex functionals, and we prove that their Gamma-liminf is bounded from below by a positive multiple of the Sobolev norm or the total var…