Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains
Spectral Theory
2025-08-11 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2407.11808,
title = {Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains},
author = {Rupert L. Frank and Simon Larson},
journal= {arXiv preprint arXiv:2407.11808},
year = {2025}
}