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arXiv · 2407.11808

Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains

Rupert L. Frank·Simon Larson
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Abstract

We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems.

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BibTeXRIS

Rupert L. Frank, Simon Larson. 2024-07-16. Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains. https://arxiv.org/abs/2407.11808

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