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

By Janna Lierl and Laurent Saloff-Coste

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 coefficients in inner uniform domains in $\mathbb R^n$. 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.Comment: Revisio

Topics: Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics - Probability
Year: 2014
OAI identifier: oai:arXiv.org:1210.4586
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