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Soeren Fournais; Bernard Helffer
Strong diamagnetism for general domains and application
(Diamagnétisme fort pour des domaines généraux et applications)
Annales de l'institut Fourier, 57 no. 7 (2007), p. 2389-2400, doi: 10.5802/aif.2337
Article PDF | Reviews MR 2394546 | Zbl 1133.35073
Class. Math.: 35P15, 35J55, 82D55
Keywords: Spectral theory, bottom of the spectrum, Neumann condition, superconductivity

Résumé - Abstract

We consider the Neumann Laplacian with constant magnetic field on a regular domain in $\mathbb{R}^2$. Let $B$ be the strength of the magnetic field and let $\lambda _1(B)$ be the first eigenvalue of this Laplacian. It is proved that $B \mapsto \lambda _1(B)$ is monotone increasing for large $B$. Together with previous results of the authors, this implies the coincidence of all the “third” critical fields for strongly type 2 superconductors.

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