8 papers
Another look at a notion of fractional mass in codimension two
Michele Caselli, Mattia Freguglia, Nicola Picenni
We study a notion of fractional -mass for codimension-two currents on closed Riemannian manifolds, defined via energy minimization with a prescribed Jacobian constraint. We prov…
Saddle solution to the complex Ginzburg-Landau system in three dimensions
Michele Caselli, Nicola Picenni
We construct an entire saddle solution to the non-magnetic complex Ginzburg-Landau system in three dimensions, whose zero set is the union of two perpendicular, intersecting lines,…
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…
Coercivity and Gamma-convergence of the -energy of sphere-valued Sobolev maps
Michele Caselli, Mattia Freguglia, Nicola Picenni
We consider sequences of maps from an -dimensional domain into the -sphere, which satisfy a natural -energy growth, as approaches from below. We prove that…
A nonlocal approximation of the area in codimension two
Michele Caselli, Mattia Freguglia, Nicola Picenni
For we introduce a notion of fractional -mass on -dimensional closed, orientable surfaces in . Moreover, we prove its -convergence, with respect to…
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…