A weighted lp-theory for second-order parabolic and elliptic partial differential systems on a half space

Kyeong Hun Kim, Kijung Lee

Research output: Contribution to journalArticle

Abstract

In this article we consider parabolic systems and Lp regularity of the solutions. With zero boundary condition the solutions experience bad regularity near the boundary. This article addresses a possible way of describing the regularity nature. Our space domain is a half space and we adapt an appropriate weight into our function spaces. In this weighted Sobolev space setting we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations. Using these, we prove uniqueness and existence results for second-order elliptic and parabolic partial differential systems in weighed Sobolev spaces.

Original languageEnglish
Pages (from-to)761-794
Number of pages34
JournalCommunications on Pure and Applied Analysis
Volume15
Issue number3
DOIs
Publication statusPublished - 2016 May 1

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Keywords

  • Elliptic partial differential systems
  • Fefferman-Stein theorem
  • Hardy-Littlewood theorem
  • Lp-theory
  • Parabolic partial differential systems
  • Sharp function estimates
  • Weighted Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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