The Dirichlet heat kernel in inner uniform domains: Local results, compact domains and non-symmetric forms

Abstract

This paper provides sharp Dirichlet heat kernel estimates in inner uniform domains, including bounded inner uniform domains, in the context of certain (possibly non-symmetric) bilinear forms resembling Dirichlet forms. For instance, the results apply to the Dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable real coefficients in inner uniform domains in Rn. The results are applicable to any convex domain, to the complement of any convex domain, and to more exotic examples such as the interior and exterior of the snowflake.