The trace of the heat kernel in lipschitz domains

Russell M. Brown

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

The trace of the heat kernel in lipschitz domains

Russell M. Brown

Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We establish the existence of an asymptotic expansion as t ⤒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 C¹-domains.

Original language	English
Pages (from-to)	889-900
Number of pages	12
Journal	Transactions of the American Mathematical Society
Volume	339
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9947-1993-1134755-9
State	Published - Oct 1993

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9947-1993-1134755-9

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abstract = "We establish the existence of an asymptotic expansion as t ⤒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 C1-domains.",

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AB - We establish the existence of an asymptotic expansion as t ⤒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 C1-domains.

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

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The trace of the heat kernel in lipschitz domains

Abstract

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