Gradient Estimates Via The Wolff Potentials For A Class Of Quasilinear Elliptic Equations

In this paper we obtain the pointwise gradient estimates via the nonlinear Wolff potentials for weak solutions of a class of non-homogeneous quasilinear elliptic equations with measure data.We divide this paper into three parts.In the first chapter,we mainly introduce the research background of PDEs and the regularity theory of quasilinear elliptic equations.The second chapter is the preliminary knowledge of this paper,including some basic concepts and basic inequalities in partial differential equations.In the last chapter,we mainly study the pointwise gradient estimates for weak solutions of the following non-homogeneous quasilinear elliptic equations with measure data div(α(|Du|)Du)=,χ∈Ω.