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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The trace of the heat kernel in Lipschitz domains


Author: Russell M. Brown
Journal: Trans. Amer. Math. Soc. 339 (1993), 889-900
MSC: Primary 58G11; Secondary 35P05, 58G18, 58G25
MathSciNet review: 1134755
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Abstract: We establish the existence of an asymptotic expansion as $ t \to {0^ + }$ for the trace of the heat kernel for the Neumann Laplacian in a bounded Lipschitz domain. The proof of an asymptotic expansion for the heat kernel for the Dirichlet Laplacian is also sketched. The treatment of the Dirichlet Laplacian extends work of Brossard and Carmona who obtained the same result in $ {C^1}$-domains.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1134755-9
PII: S 0002-9947(1993)1134755-9
Article copyright: © Copyright 1993 American Mathematical Society