Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

Krzysztof Bogdan; Tomasz Grzywny; Michał Ryznar

doi:10.1214/10-AOP532

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Home > Journals > Ann. Probab. > Volume 38 > Issue 5 > Article

September 2010 Heat kernel estimates for the fractional Laplacian with Dirichlet conditions

Krzysztof Bogdan, Tomasz Grzywny, Michał Ryznar

Ann. Probab. 38(5): 1901-1923 (September 2010). DOI: 10.1214/10-AOP532

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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.

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Krzysztof Bogdan. Tomasz Grzywny. Michał Ryznar. "Heat kernel estimates for the fractional Laplacian with Dirichlet conditions." Ann. Probab. 38 (5) 1901 - 1923, September 2010. https://doi.org/10.1214/10-AOP532

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Published: September 2010

First available in Project Euclid: 17 August 2010

zbMATH: 1204.60074

MathSciNet: MR2722789

Digital Object Identifier: 10.1214/10-AOP532

Subjects:

Primary: 60J35 , 60J50

Secondary: 31B25 , 60J75

Keywords: boundary Harnack principle , Dirichlet problem , fractional Laplacian , Heat kernel estimate , Lipschitz domain

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Vol.38 • No. 5 • September 2010

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Krzysztof Bogdan, Tomasz Grzywny, Michał Ryznar "Heat kernel estimates for the fractional Laplacian with Dirichlet conditions," The Annals of Probability, Ann. Probab. 38(5), 1901-1923, (September 2010)

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