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Estimates of Dirichlet heat kernel for symmetric Markov processes

Author

Listed:
  • Grzywny, Tomasz
  • Kim, Kyung-Youn
  • Kim, Panki

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.

Suggested Citation

  • Grzywny, Tomasz & Kim, Kyung-Youn & Kim, Panki, 2020. "Estimates of Dirichlet heat kernel for symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 431-470.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:431-470
    DOI: 10.1016/j.spa.2019.03.017
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    References listed on IDEAS

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    1. Bogdan, Krzysztof & Grzywny, Tomasz & Ryznar, Michał, 2014. "Dirichlet heat kernel for unimodal Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3612-3650.
    2. Kim, Panki & Song, Renming & Vondraček, Zoran, 2014. "Global uniform boundary Harnack principle with explicit decay rate and its application," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 235-267.
    3. Kim, Kyung-Youn & Kim, Panki, 2014. "Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in C1,η open sets," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3055-3083.
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