Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian

2024/05/20 by Vladimir Lotoreichik, Lotoreichik, Vladimir · 1 citation
Mathematics · Computer Science · Materials Science · #Spectral Theory in Mathematical Physics #Advanced Mathematical Modeling in Engineering #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.2405.12077

Abstract

We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the (k+1)-th magnetic Neumann eigenvalue of a bounded convex planar domain is not larger than its k-th magnetic Dirichlet eigenvalue. In three dimensions, we restrict our attention to convex domains, which are invariant under rotation by an angle of π around an axis parallel to the magnetic field. For such domains, we prove that the (k+2)-th magnetic Neumann eigenvalue is not larger than the k-th magnetic Dirichlet eigenvalue provided that this Dirichlet eigenvalue is simple. The proofs rely on a modification of the strategy due to Levine and Weinberger.

Cited by

• The Levine--Weinberger and Friedlander--Filonov inequalities for some classes of elliptic operators

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