Regularity For Weak And Very Weak Solutions Of Obstacle Problems

This thesis mainly studies the local regularity for weak solutions of Kψ,θp-obstacle problems to the equation divA(x,▽u)= 0 and the local regularity for very weak solutions of obstacle problems of non-homogeneous elliptic equation divA(x,▽u)=B(x,▽u),It is consisted of four chapters.We briefly address the background and history of weak and very weak solutions for obstacle problems in the first chapter,We also give the main work of this paper.In the second chapter we introduce some preliminary knowledges we neededIn the third chapter we consider the local regularity for weak solutions of Kψ,θp-obstacle problems to the equation divA(x,▽u)=0 by means of using cutoff function and Young inequality,This result is an improvement of H.Y.Gao and H.Y.Tian.In the last chapter we obtain the local regularity for very weak solutions of non-homogeneous elliptic equation divA(x,▽u)=B(x,▽u) by using Hodge decomposition to construct test function and Young inequality,Holder inequality, Poincare inequality This result generalize the one of H.Y.Gao,M.Wang and H.L.Zhao.