Subexponential behaviour of the Dirichlet heat kernel

摘要

We obtain a formula for the asymptotic behaviour of the Dirichlet heat kernel for large time in terms of the survival probability of a Brownian motion, under the assumption that the latter decays subexponentially for large time. We also obtain a lower bound for the Dirichlet heat kernel for arbitrary open and connected sets in Euclidean space. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 9]