Riesz potential type estimates for nonlinear elliptic equations

Abstract

For p≥2, we study nonlinear elliptic equations of p-Laplacian type with measure datadiv 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.