The density of superconductivity in domains with corners

TL;DR

This paper analyzes how superconductivity density concentrates near corners in a planar domain under a uniform magnetic field, using Ginzburg-Landau theory for large parameters.

Contribution

It provides explicit computations of the superconductivity density in domains with corners, focusing on the regime where superconductivity is localized near these corners.

Findings

Superconductivity concentrates near corners in the specified regime.

Explicit formulas for the L^2-norm of the minimizer are derived.

Results are valid for large Ginzburg-Landau parameters and uniform magnetic fields.

Abstract

We compute the $L^2$-norm of the minimizer of the Ginzburg-Landau functional in a planar domain with a finite number of corners. Our computations are valid for a uniform applied magnetic field, large Ginzburg-Landau parameter and in the regime where superconductivity is confined near the corners of the domain.