Global heat kernel estimate for relativistic stable processes in exterior open sets

Zhen Qing Chen*, Panki Kim, Renming Song

*Corresponding author for this work

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Abstract

In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets are established for all time t>0. These transition densities are also the Dirichlet heat kernels of m-(m 2/α-δ) α/2 with m∈(0, 1] in C 1,1 exterior open sets. The estimates are uniform in m in the sense that the constants are independent of m∈(0, 1]. As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic α-stable processes with mass m∈(0, 1] in C 1,1 exterior open sets.

Original languageEnglish
Pages (from-to)448-475
Number of pages28
JournalJournal of Functional Analysis
Volume263
Issue number2
DOIs
Publication statusPublished - 15 Jul 2012
Externally publishedYes

Keywords

  • Exit time
  • Green function
  • Heat kernel
  • Lévy system
  • Parabolic Harnack inequality
  • Relativistic stable process
  • Symmetric α-stable process
  • Transition density

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Chen, Z. Q., Kim, P., & Song, R. (2012). Global heat kernel estimate for relativistic stable processes in exterior open sets. Journal of Functional Analysis, 263(2), 448-475. https://doi.org/10.1016/j.jfa.2012.04.012