The trace of the heat kernel in Lipschitz domains

Brown, Russell M.

doi:10.1090/S0002-9947-1993-1134755-9

The trace of the heat kernel in Lipschitz domains
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by Russell M. Brown PDF

Trans. Amer. Math. Soc. 339 (1993), 889-900 Request permission

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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