Spectral asymptotics of the Neumann Laplacian with variable magnetic field on a smooth bounded domain in three dimensions
Maha Aafarani, Khaled Abou Alfa, Frédéric Hérau, Nicolas Raymond · Analysis & PDE · 2025
This article is devoted to 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.