A Ginzburg-Landau type energy with weight and with convex potential near zero

TL;DR

This paper investigates the asymptotic behavior and energy estimates of solutions to a weighted Ginzburg-Landau functional with convex potential near zero, extending known lower bounds for unit vector fields.

Contribution

It introduces a generalized energy lower bound for weighted Ginzburg-Landau functionals with convex potentials near zero, expanding previous results.

Findings

Derived asymptotic behavior of minimizers

Provided energy estimates for the functional

Extended Brezis-Merle-Rivière lower bound

Abstract

In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower bound for the energy of unit vector field given initially by Brezis-Merle-Rivi\`ere.