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 journalArticlepeer-review

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

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

Fingerprint Dive into the research topics of 'A weighted lp-theory for second-order parabolic and elliptic partial differential systems on a half space'. Together they form a unique fingerprint.

Cite this