Eigenvalues of the Magnetic Neumann Laplacian on Domains with Peaks

Noah Koerner

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arXiv · 2608.09469

Eigenvalues of the Magnetic Neumann Laplacian on Domains with Peaks

Noah Koerner

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Abstract

We consider the magnetic Neumann Laplacian on bounded domains in $\mathbb{R}^2$ with outward peaks. The operator is associated with a large magnetic field depending on a parameter $\lambda$, and we investigate the behaviour of the eigenvalues as $\lambda$ tends to $+\infty$. We show that their asymptotic expansion is influenced by the sharpness $q$ and geometry of the peak, and that its main term is of order $\lambda^{\frac{2}{q+1}}$. This is an extension of previous works on magnetic Neumann Laplacians in smooth domains and domains with corners.

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BibTeX RIS

Noah Koerner. 2026-08-10. Eigenvalues of the Magnetic Neumann Laplacian on Domains with Peaks. https://arxiv.org/abs/2608.09469

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