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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. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1901.09771arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Additional Information:© 2019 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. 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:http://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218
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:20 May 2019 20:40

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