Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

Krzysztof Bogdan, Tomasz Grzywny, and Michał Ryznar

Source: Ann. Probab. Volume 38, Number 5 (2010), 1901-1923.

Abstract

We give sharp estimates for the heat kernel of the fractional Laplacian with Dirichlet condition for a general class of domains including Lipschitz domains.

First Page: Show

Primary Subjects: 60J35, 60J50

Secondary Subjects: 60J75, 31B25

Keywords: Fractional Laplacian; Dirichlet problem; heat kernel estimate; Lipschitz domain; boundary Harnack principle

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Permanent link to this document: http://projecteuclid.org/euclid.aop/1282053775
Digital Object Identifier: doi:10.1214/10-AOP532
Mathematical Reviews number (MathSciNet): MR2722789
Zentralblatt MATH identifier: 05793425

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