Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain
Journal article, 2020
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.
Author
Rupert L. Frank
Ludwig Maximilian University of Munich (LMU)
California Institute of Technology (Caltech)
Simon Larson
Royal Institute of Technology (KTH)
Published in
Journal fur die Reine und Angewandte Mathematik
00754102 (ISSN) 14355345 (eISSN)
Vol. 766 p. 195-228Categorizing
Subject Categories (SSIF 2011)
Mathematical Analysis
Identifiers
DOI
10.1515/crelle-2019-0019