Global weighted estimates for the gradient of solutions to nonlinear elliptic equations

Sun Sig Byun, Seungjin Ryu

Research output: Contribution to journalArticlepeer-review

68 Scopus citations

Abstract

We consider nonlinear elliptic equations of p-Laplacian type that are not necessarily of variation form when the nonlinearity is allowed to be discontinuous and the boundary of the domain can go beyond the Lipschitz category. Under smallness in the BMO nonlinearity and sufficient flatness of the Reifenberg domain, we obtain the global weighted Lq estimates with qε(p,∞) for the gradient of weak solutions.

Original languageEnglish
Pages (from-to)291-313
Number of pages23
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume30
Issue number2
DOIs
StatePublished - 2013

Keywords

  • BMO space
  • Gradient estimate
  • Nonlinear elliptic equation
  • Reifenberg domain

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