Global gradient estimates for nonlinear elliptic equations

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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
Issue number6
StatePublished - 2014


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


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