On Lp-estimates for a class of non-local elliptic equations

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

We consider non-local elliptic operators with kernel K(y)=a(y)/|y|d+σ, where 0<σ<2 is a constant and a is a bounded measurable function. By using a purely analytic method, we prove the continuity of the non-local operator L from the Bessel potential space Hpσ to Lp, and the unique strong solvability of the corresponding non-local elliptic equations in Lp spaces. As a byproduct, we also obtain interior Lp-estimates. The novelty of our results is that the function a is not necessarily to be homogeneous, regular, or symmetric. An application of our result is the uniqueness for the martingale problem associated to the operator L.

Original languageEnglish
Pages (from-to)1166-1199
Number of pages34
JournalJournal of Functional Analysis
Volume262
Issue number3
DOIs
Publication statusPublished - 2012 Feb 1

Keywords

  • Bessel potential spaces
  • Lévy processes
  • Non-local elliptic equations
  • The martingale problem

ASJC Scopus subject areas

  • Analysis

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