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

    1 Citation (Scopus)

    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

    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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