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This article is devoted the semiclassical spectral analysis of the Neumannmagnetic Laplacian on a smooth bounded domain in three dimensions. Under ageneric assumption on the variable magnetic field (involving a localization ofthe eigenfunctions near the boundary), we establish a semiclassical expansionof the lowest eigenvalues. In particular, we prove that the eigenvalues becomesimple in the semiclassical limit.

Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions