Estimates of Dirichlet heat kernel for symmetric Markov processes

Tomasz Grzywny, Kyung-Youn Kim and Panki Kim

Stochastic Processes and their Applications, 2020, vol. 130, issue 1, 431-470

Abstract: We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in C1,1 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 C1,1 open sets.

Keywords: First exit time; Dirichlet heat kernel; Heat kernel; Markov process; Transition density; Green function; Boundary Harnack inequality (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.03.017

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