Estimates of Dirichlet heat kernel for symmetric Markov processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Grzywny, Tomasz¹  Kim, Kyung-Youn²  Kim, Panki^3,4 

[1] Wroclaw Univ Sci & Technol, Dept Pure & Appl Math, Wybrzeze Wyspianskiego 27, PL-50370 Wroclaw, Poland

[2] Bielefeld Univ, Fac Math, Univ Str 25, D-33615 Bielefeld, Germany

[3] Seoul Natl Univ, Dept Math Sci, Bldg 27,1 Gwanak Ro, Seoul 151747, South Korea

[4] Seoul Natl Univ, Res Inst Math, Bldg 27,1 Gwanak Ro, Seoul 151747, South Korea

关键词: First exit time;    Dirichlet heat kernel;    Heat kernel;    Markov process;    Transition density;    Green function;    Boundary Harnack inequality;   

DOI  :  10.1016/j.spa.2019.03.017

来源: Elsevier

【 摘 要 】

We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Levy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in C-1,C-1 open sets. As corollaries of our main results, we obtain sharp two-sided Green function estimates and a scale invariant boundary Harnack inequality with explicit decay rates in C-1,C-1 open sets. (C) 2019 Published by Elsevier B.V.

【 授权许可】

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