Strong diamagnetism for general domains and applications

Abstract

We consider the Neumann Laplacian with constant magnetic field on a regular domain. Let $B$ be the strength of the magnetic field, and let ${\lambda }_1(B)$ be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that $B\mapsto {\lambda }_1(B)$ is monotone increasing for large $B$. Combined with the results of \cite{FournaisHelffer3}, this implies that all the `third' critical fields for strongly Type II superconductors coincide.

A few typos corrected. One argument given in more details. Version to be published in AIF

Cited by in corpus (1)

• On the stability of normal states for a generalized Ginzburg-Landau model