The trace of the heat kernel in Lipschitz domains

Abstract

We establish the existence of an asymptotic expansion as t → 0 + 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 {C^1} -domains.