Global gradient estimates for nonlinear elliptic equations

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Abstract

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calderón-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

Original languageEnglish
Pages (from-to)1209-1220
Number of pages12
JournalJournal of the Korean Mathematical Society
Volume51
Issue number6
DOIs
StatePublished - 2014

Keywords

  • BMO space
  • Calderón-Zygmund theory
  • Global gradient estimate
  • Nonlinear elliptic equation
  • Reifenberg flat domain

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