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

Author:

Frank Rupert L.1ORCID,Larson Simon2ORCID

Affiliation:

1. Mathematisches Institut , Ludwig-Maximilans Universität München , Theresinstr. 39, 80333 München , Germany ; and Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

2. Department of Mathematics , KTH Royal Institute of Technology , SE-100 44 Stockholm , Sweden

Abstract

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.

Funder

National Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

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3. R. Bañuelos, T. Kulczycki and B. O. Siudeja, On the trace of symmetric stable processes on Lipschitz domains, J. Funct. Anal. 257 (2009), no. 10, 3329–3352.

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