Regularity In Morrey Spaces For Nonlinear Elliptic Equations With VMO Independent Variables

In my dissertation,I mainly study some regularity in Morrey spaces for nonlinear elliptic equations with VMO independent variables.we will present interior regularity and boundary regularity in Morrey spaces for the solutions of nonlinear elliptic systems of second order,we will consider systems of the form for Ωa bounded domain in RN,≥2,(?)Ω∈C2,1,f∈l2,λ(Ω,RN),0<λ<n. The paper is made up of four parts as follows:In the first chapter, we briefly introduce the development of the regularity of elliptic equation (systems) in Morrey space and the background of selecting this question.The second chapter, we shall give some basic definitions and some related lem-mas which we use in this paper.The third chapter, we shall extend the interior estimates in Morrey spaces for non-linear equations with continuous coefficients to the following non-linear equa-tions with VMO coefficient in dependent variables.The Morrey estimate as follows: f∈L2,λ(Ω,RN),],μ∈(0,λ],μ<n∈.The forth chapter,we shall study the boundary regularity in Morrey spaces for the solutions of non-linear elliptic systems of second order.In this section,we will present full regularity in Morrey spaces. (当γ＋δ→0＋时,∈→1),x0∈(?)Ω.In my paper,we will prove in the method of the trace of Korn.the method was used in the paper of non-linear elliptic problem by Campanato[1,10].In my disserta-tion, we will estimate the norm of D2u in Morrey spaces in order to prove the interior regularity.And,in ma paper,we study the elliptic problems with discontinuous coef-ficients.