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

T. Schmatzler

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arXiv · 2506.09468

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

T. Schmatzler

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Abstract

We consider the eigenvalue problem for certain classes of elliptic operators, namely inhomogeneous membrane operators $ L = \tfrac{1}{ \rho } ( -\Delta + V ) $ and divergence form operators $ L = -\operatorname{div} A \nabla $, on bounded domains. For these operators, we prove ordering inequalities between the Dirichlet and the Neumann eigenvalues, generalizing results of Levine--Weinberger and Friedlander--Filonov for the Laplacian. We take inspiration from their proofs and derive sufficient conditions on the coefficients of the operator that ensure that the inequalities remain valid.

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BibTeX RIS

T. Schmatzler. 2025-06-11. The Levine--Weinberger and Friedlander--Filonov inequalities for some classes of elliptic operators. https://arxiv.org/abs/2506.09468

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