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 λ1(B) be the first eigenvalue of the magnetic Neumann Laplacian on the domain. It is proved that B λ1(B) is monotone increasing for large B. Combined with the results of FournaisHelffer3, this implies that all the `third' critical fields for strongly Type II superconductors coincide.
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