3 papers
math.AP2025
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,…
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
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…