Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift

Yasunori Maekawa, Hideyuki Miura

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We consider some non-local diffusion equations in the presence of a divergence free drift term, where the diffusion operators are related to certain Dirichlet forms of jump type. We derive pointwise upper bounds for fundamental solutions of the equations under weak assumptions for the velocity of the drift term. Our class of the velocity includes functions with the scale-critical regularity and some growing functions at spatial infinity.

Original languageEnglish
Pages (from-to)2245-2268
Number of pages24
JournalJournal of Functional Analysis
Volume264
Issue number10
DOIs
Publication statusPublished - 2013 May 15

Keywords

  • Divergence free drift
  • Fundamental solutions
  • Non-local diffusion
  • Pointwise upper bound

ASJC Scopus subject areas

  • Analysis

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