Regularity of the Very Weak Solutions for Double Obstacle Problems

The apply of harmonic eauation is know to all. Our interesting is to get the regularity os their solution, recently for obstacle problems. Many interesting results have been obtained for the solutions of harmonic equation ande their obstacle problems, however the double obstacle ploblems about the definition and regularity results for non-homogeneous elliptic equation. In this paper, the basic tool for the Young inequality,Holder inequality, Minkowski inequality, Poincare inequality and a basic inequality. The definition of very weak solutions for double obstacle problems associated with non-homogeneous elliptic equation is given, and the local integrability result is obtained by using the technique of Hodge decomposition.