Gradient estimates and their optimality for heat equation in an exterior domain

Vladimir Georgiev, Koichi Taniguchi

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet problem. Applications of these estimates to bilinear type commutator estimates for Laplace operator with Dirichlet boundary condition in exterior domain are discussed too.

MSC Codes 35K05 (Primary), 35K20 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 Oct 2

Keywords

  • Dirichlet problem
  • Exterior domains
  • Gradient estimates
  • Heat equations

ASJC Scopus subject areas

  • General

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