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arXiv · 1210.4586

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

Janna Lierl·Laurent Saloff-Coste
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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.

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BibTeXRIS

Janna Lierl, Laurent Saloff-Coste. 2012-10-16. The Dirichlet heat kernel in inner uniform domains: local results, compact domains and non-symmetric forms. https://arxiv.org/abs/1210.4586

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