Heat kernel estimates for dirichlet fractional laplacian with gradient perturbation

Peng Chen, Renming Song, Longjie Xie, Yingchao Xie

Research output: Contribution to journalArticlepeer-review

Abstract

We give a direct proof of the sharp two-sided estimates, recently established in [4,9], for the Dirichlet heat kernel of the fractional Laplacian with gradient perturbation in C 1,1 open sets by using Duhamel's formula. We also obtain a gradient estimate for the Dirichlet heat kernel. Our assumption on the open set is slightly weaker in that we only require D to be C 1,θ for some θ ∈ (α/2,1].

Original languageEnglish (US)
Pages (from-to)91-111
Number of pages21
JournalJournal of the Korean Mathematical Society
Volume56
Issue number1
DOIs
StatePublished - Jan 1 2019

Keywords

  • Dirichlet heat kernel
  • Fractional Laplacian
  • Gradient estimate
  • Isotropic stable process
  • Kato class

ASJC Scopus subject areas

  • Mathematics(all)

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