Gradient estimates for higher order elliptic equations on nonsmooth domains

Sun Sig Byun, Seungjin Ryu

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We establish optimal gradient estimates in Orlicz space for a nonhomogeneous elliptic equation of higher order with discontinuous coefficients on a nonsmooth domain. Our assumption is that for each point and for each sufficiently small scale the coefficients have small mean oscillation and the boundary of the domain is sufficiently close to a hyperplane. As a consequence we prove the classical Wm,p, m=1,2,..., 1<p<∞, estimates for such a higher order equation. Our results easily extend to higher order elliptic and parabolic systems.

Original languageEnglish
Pages (from-to)243-263
Number of pages21
JournalJournal of Differential Equations
Volume250
Issue number1
DOIs
StatePublished - 1 Jan 2011

Keywords

  • BMO space
  • Gradient estimate
  • Higher order equation
  • Orlicz space
  • Primary
  • Reifenberg domain
  • Reverse Hölder inequality
  • Secondary

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