7 citations · 15 across the 14 of their papers we have counts for
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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…
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…
Staircasing effect for minimizers of the one-dimensional discrete Perona-Malik functional
Nicola Picenni
We consider the one-dimensional Perona-Malik functional, that is the energy associated to the celebrated forward-backward equation introduced by P. Perona and J. Malik in the conte…
Monotonicity properties of limits of solutions to the semi-discrete scheme for the Perona-Malik equation
Massimo Gobbino, Nicola Picenni
We consider generalized solutions of the Perona-Malik equation in dimension one, defined as all possible limits of solutions to the semi-discrete approximation in which derivatives…
A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona-Malik functional
Massimo Gobbino, Nicola Picenni
We consider the Perona-Malik functional in dimension one, namely an integral functional whose Lagrangian is convex-concave with respect to the derivative, with a convexification th…