Heat kernel for the elliptic system of linear elasticity with boundary conditions

Justin Taylor, Seick Kim, Russell Brown

Research output: Contribution to journalArticle

Abstract

We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.

Original languageEnglish
Pages (from-to)2485-2519
Number of pages35
JournalJournal of Differential Equations
Volume257
Issue number7
DOIs
Publication statusPublished - 2014 Oct 1

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Heat kernel for the elliptic system of linear elasticity with boundary conditions'. Together they form a unique fingerprint.

  • Cite this