Riesz potential type estimates for nonlinear elliptic equations

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For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure data div a(Du,u,x)=μ in Ω when the nonlinearity depends on the variable of the possibly unbounded solution itself. We obtain the point-wise gradient bound and the gradient continuity in terms of a certain Riesz potential of the right-hand side measure.

Original languageEnglish
Pages (from-to)6844-6884
Number of pages41
JournalJournal of Differential Equations
Issue number10
StatePublished - 15 Nov 2017


  • Nonlinear elliptic equations
  • Riesz potential type estimates


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