A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in Rd

Kyeong Hun Kim, Kijung Lee, Jinsol Seo

Research output: Contribution to journalArticlepeer-review

Abstract

We establish existence, uniqueness, and arbitrary order Sobolev regularity results for the second order parabolic equations with measurable coefficients defined on the conic domains D of the type D(M):={x∈Rd:[Formula presented]∈M},M⊂Sd−1. We obtain the regularity results by using a system of mixed weights consisting of appropriate powers of the distance to the vertex and of the distance to the boundary. We also provide the sharp ranges of admissible powers of the distance to the vertex and to the boundary.

Original languageEnglish
Pages (from-to)154-194
Number of pages41
JournalJournal of Differential Equations
Volume291
DOIs
Publication statusPublished - 2021 Aug 5

Keywords

  • Conic domains
  • Measurable coefficients
  • Mixed weight
  • Parabolic equation
  • Weighted Sobolev regularity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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