Michele Caselli

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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

Stable $s$ -minimal cones in $R^{2}$ are flat for $s \sim 0$

Michele Caselli

For $s \in (0, 1)$ small, we show that the only cones in $R^{2}$ stationary for the $s$ -perimeter and stable in $R^{2} ∖ {0}$ are half-planes. This is in dir…

math.AP2025

Coercivity and Gamma-convergence of the $p$ -energy of sphere-valued Sobolev maps

Michele Caselli, Mattia Freguglia, Nicola Picenni

We consider sequences of maps from an $(n + m)$ -dimensional domain into the $(n - 1)$ -sphere, which satisfy a natural $p$ -energy growth, as $p$ approaches $n$ from below. We prove that…

Saddle solution to the complex Ginzburg-Landau system in three dimensions

Stable s-minimal cones in R2 are flat for s∼0

Coercivity and Gamma-convergence of the p-energy of sphere-valued Sobolev maps

Stable $s$ -minimal cones in $R^{2}$ are flat for $s \sim 0$

Coercivity and Gamma-convergence of the $p$ -energy of sphere-valued Sobolev maps