Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions
arXiv (Cornell University)(2023)
Abstract
This article is devoted the semiclassical spectral analysis of the Neumann magnetic Laplacian on a smooth bounded domain in three dimensions. Under a generic assumption on the variable magnetic field (involving a localization of the eigenfunctions near the boundary), we establish a semiclassical expansion of the lowest eigenvalues. In particular, we prove that the eigenvalues become simple in the semiclassical limit.
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Key words
neumann laplacian,spectral asymptotics
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