Gradient Estimates For Weak Solutions Of A Class Of Elliptic Equations

Partial differential equations are widely used in mathematics,physics,mechanics,engineering and other relative fields.And they are mainly divided into three categories: elliptic equations,parabolic equations and hyperbolic equations.Gradient estimates play an important role in the theoretical study of elliptic and parabolic partial differential equations.The main purpose is to study the gradient estimates of the weak solutions of elliptic equations.The gradient estimates for weak solutions to non-homogeneous A-harmonic equations under natural growth and the gradient estimates for weak solutions to the obstacle problems corresponding to a class of A-harmonic equations are both obtained.The specific contents are as follows.Chapter 1 begins with the research background and the present situation at home and abroad.Besides,the research scheme and the design concept of the system are discussed.Chapter 2 introduces the related concepts and the main results.In Chapter 3,the gradient estimates for weak solutions to non-homogeneous Aharmonic equations under natural growth are established.And pL-type estimates and gradient estimates in Orlicz space are derived.The research method is the iterationcovering procedure.Chapter 4 deals with the gradient estimates for weak solutions to a class of Aharmonic equations.pL-type estimates to the obstacle problems corresponding to such equation are derived.The L?-type estimates in Orlicz space are also derived by a new normalization method and the iteration-covering procedure.This is an extension for classical theorem.Finally,the main conclusions are given and the further research problems are discussed.Figure 0;Table 0;Reference 61...