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

Frank, Rupert L. and Larson, Simon (2019) Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain. Journal für die reine und angewandte Mathematik . ISSN 0075-4102. (In Press) https://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1515/crelle-2019-0019DOIArticle
https://arxiv.org/abs/1901.09771arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Larson, Simon0000-0002-0057-8211
Additional Information:© 2019 Walter de Gruyter GmbH, Berlin/Boston. Received: 2019-02-26; Revised: 2019-05-12; Published Online: 2019-08-15. U.S. National Science Foundation grant DMS-1363432 (R.L.F.) and Swedish Research Council grant no. 2012-3864 (S.L.) is acknowledged.
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
Swedish Research Council2012-3864
Classification Code:2010 Mathematics Subject Classification: 35P20
Record Number:CaltechAUTHORS:20190520-133710218
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218
Official Citation:Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2019-0019
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:95606
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 May 2019 20:40
Last Modified:03 Oct 2019 21:15

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