Some Properties For Weak Solutions And Very Weak Solutions Of Obstacle Problems

The properties for(very)weak solution of obstacle problems to the A-harmonic equation have been studied by many people recently.This thesis mainly studies some properties for weak solutions and very weak solutions of obstacle problems of nonhomogeneous A-harmonic equations.It is consisted of five chapters.In Chapter 1,which serves as the introduction,the background and history of weak solutions and very weak solutions for obstacle problems are briefly addressed, and the main work of this paper is given.In Chapter 2,we introdue some preliminary knowledges we need.In Chapter 3,by means of using cutoff function and Young inequality,we consider the local regularity for weak solutions of obstacle problems to the equation divA(x,â–½u(x))= divF(x).The result is an improvement in[37].In Chapter 4,using Hodge decomposition to construct test function and using Young inequality,Sobolev inequality,we obtain the local regularity for weak solutions of obatacle problems to the equation divA(x,â–½u(x))= divF(x,u).This result generalized the one in[2].In Chapter 5,we consider the equation divA(x,â–½u(x))= F(x),and obtain a quasi-minimizer of the p-Dirichlet integral estimate of weak solutions for obstacle problems.The result is an improvement in[31].