Existence Of Entropy Solutions For Elliptic Equations With P(X)-Growth

With the development of elastic mechanics, the problems of elliptic partial differential equation with nonstandard growth conditions have attracted much attenttion. As a special case of nonstandard growth conditions, p(x)-growth conditions have been applied in nonlinear elasticity and non-Newtonian fluids, which make important practical significance to studying existence of entropy solutions of elliptic problems .In this dissertation, by means of the basic theory of generalized Lebesuge space L^p(x)(Ω) and generalized Sobolev space W^m,p(x)(Ω) , we study the existence of solution for the Dirichlet problem of elliptic partial differential equations: where b:[0,+∞)→[0,+∞) is a non-decreasing continuous function,c(x) is nonnegative constant function.