Harnack inequality and interior regularity for Markov processes with degenerate jump kernels

Panki Kim, Renming Song, Zoran Vondraček

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study interior potential-theoretic properties of purely discontinuous Markov processes in proper open subsets D⊂Rd. The jump kernels of the processes may be degenerate at the boundary in the sense that they may vanish or blow up at the boundary. Under certain natural conditions on the jump kernel, we show that the scale invariant Harnack inequality holds for any proper open subset D⊂Rd and prove some interior regularity of harmonic functions. We also prove a Dynkin-type formula and several other interior results.

Original languageEnglish (US)
Pages (from-to)138-180
Number of pages43
JournalJournal of Differential Equations
Volume357
DOIs
StatePublished - Jun 5 2023

Keywords

  • Harnack inequality
  • Jump kernel with boundary part
  • Jump processes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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