Bulk superconductivity in Type II superconductors near the second critical field

TL;DR

This paper establishes a new $L^{ infty}$ estimate for the order parameter in bulk Type II superconductors near the second critical field, addressing an open problem and advancing understanding of the transition between superconducting states.

Contribution

It provides the first $L^{ infty}$ estimate in the bulk of Type II superconductors near the second critical field, solving an open problem in the field.

Findings

Proves a new $L^{ infty}$ estimate for the order parameter in the bulk.

Addresses the transition from bulk to surface superconductivity.

Resolves an open problem posed by Aftalion and Serfaty.

Abstract

We consider superconductors of Type II near the transition from the 'bulk superconducting' to the 'surface superconducting' state. We prove a new $L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from the boundary. This solves an open problem posed by Aftalion and Serfaty.