Decay of superconductivity away from the magnetic zero set

TL;DR

This paper provides exponential bounds on the Ginzburg-Landau order parameter away from the zero set of the magnetic field, clarifying the distribution of superconductivity in different regimes.

Contribution

It extends previous work by establishing bounds for magnetic field strengths comparable to the Ginzburg-Landau parameter, detailing superconductivity decay near the zero set.

Findings

Exponential decay bounds for the order parameter away from the zero magnetic field set.

Distribution patterns of surface and bulk superconductivity.

Results valid for Hölder continuous magnetic fields.

Abstract

We establish exponential bounds on the Ginzburg-Landau order parameter away from the curve where the applied magnetic field vanishes. In the units used in this paper, the estimates are valid when the parameter measuring the strength of the applied magnetic field is comparable with the Ginzburg-Landau parameter. This completes a previous work by the authors analyzing the case when this strength was much higher. Our results display the distribution of surface and bulk superconductivity and are valid under the assumption that the magnetic field is H\"older continuous.