Regularity estimates for higher order elliptic systems on Reifenberg flat domains

The Anh Bui, Xuan Thinh Duong, Xuan Truong Le*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    4 Citations (Scopus)

    Abstract

    Consider a higher order elliptic system{Dα(aijαβ(x)Dβuj)=DαfiαinΩ,|ui|+|Dui|+…+|Dmi−1ui|=0on∂Ω, for all i=1,…,N with N∈N+, and all multi-indices |α|=mi, |β|=mj with mi∈N+ for all i=1,…,N, and the standard summation notation is understood. We assume that the leading coefficients aijαβ(x) have small BMO norms and the domain Ω⊂RN is open, bounded and flat in the Reifenberg's sense. This article is to prove the regularity estimates of this system in weighted Lorentz spaces and in Lorentz–Morrey spaces. Our results require weak assumptions on the regularity of the coefficients aijαβ(x) and the boundary ∂Ω, and they are new even for scalar higher order elliptic equations.

    Original languageEnglish
    Pages (from-to)5637-5669
    Number of pages33
    JournalJournal of Differential Equations
    Volume261
    Issue number10
    DOIs
    Publication statusPublished - 15 Nov 2016

    Keywords

    • Higher-order elliptic systems
    • Lorentz–Morrey spaces
    • Reifenberg flat domain
    • Weighted Lorentz spaces

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