Existence And Uniqueness Of Entropy Solutions For Elliptic Equations With Variable Coefficients And Weighted L~p Estimates For The Poisson Equation

In this paper, we mainly investigate existence and uniqueness of entropy solutionsof elliptic equations with (p(x),q(x))-growth conditions and weighted Lpestimates for thePoisson equation.This paper has five chapters.The first chapter is the preface of the thesis. In this chapter we state the mainresearch subjects and their backgrounds.The second chapter is preliminaries. Here we mainly introduce the basic theory,which will be used in the third and fourth chapter.In the third chapter, we mainly study existence and uniqueness of entropy solutionsof elliptic equations with (p(x),q(x))-growth conditions in generalized Sobolev spaces. Bymeans of the basic theory of generalized Sobolev space Wk,p(x)(), we use the approximatemethod of truncation function to obtain existence of entropy solutions.In the fourth chapter, we obtain a new class of regularity estimates, weighted L~pestimates for the Poisson equation.In the last chapter, we make a summary of the third and fourth chapter.