Schauder estimates for a class of non-local elliptic equations

Hongjie Dong, Doyoon Kim

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

We prove Schauder estimates for a class of non-local elliptic operators with kernel K(y) = a(y)/|y|d+σ and either Dini or Hölder continuous data. Here 0 < σ < 2 is a constant and a is a bounded measurable function, which is not necessarily to be homogeneous, regular, or symmetric. As an application, we prove that the operators give isomorphisms between the Lipschitz-Zygmund spaces Λα+σ and Λα for any α > 0. Several local estimates and an extension to operators with kernels K(x, y) are also discussed.

Original languageEnglish
Pages (from-to)2319-2347
Number of pages29
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number6
DOIs
Publication statusPublished - 2013 Jun

Keywords

  • Lévy processes
  • Non-local elliptic equations
  • Schauder estimates

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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