Continuity of Harmonic Functions for Non-local Markov Generators

Masaki Wada

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this paper, we treat a priori estimates of harmonic functions for jump processes associated with non-local operators. Let L be a non-local operator given by Under some conditions on n(x,h), we prove the Hölder continuity and the uniform continuity of L-harmonic functions. Our results are extensions of those obtained by Bass and Kassmann (Commun Part Diff Eq 30:1249-1259, 2005).

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalPotential Analysis
Volume39
Issue number1
DOIs
Publication statusPublished - 2013 Jul 1

Keywords

  • A priori estimates
  • Continuity of harmonic functions
  • Markov jump processes
  • Martingale problem

ASJC Scopus subject areas

  • Analysis

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