Global Integrability For Solutions To Anisotropic Functionals And Obstacle Problems

The purpose of this dissertation is divided into two parts. It is to get global integrability of anisotropic functionals and obstacle problems.In the first part, we get global integrability for solutions to anisotropic functionals(?)where(?0and(?)is the gradient of u, and the energy f(x,z) is supposed to be nonnegative. The condition in this paper is weaker than that of [2], and we give a research for obstacle problems of anisotropic functionals.In the second part, we get global integrability for minimizers of obstacle problems of anisotropic functionals. We deal with minimizers(?)-obstacle problems of anisotropic functionals whose prototype is(?)We show that higher integrability of ?*=max{?,?} forces minimizers u to have integrability as well.