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arXiv · 1901.09771

Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain

Rupert L. Frank·Simon Larson
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Abstract

We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.

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Rupert L. Frank, Simon Larson. 2019-01-28. Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. https://doi.org/10.1515/crelle-2019-0019

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