ON SECOND ORDER ELLIPTIC EQUATIONS AND VARIATIONAL INEQUALITIES WITH ANISOTROPIC PRINCIPAL OPERATORS

This paper is about boundary value problems of the form {-div[del Phi(del u)] = f(x, u) in Omega, u = 0 on partial derivative Omega, where Phi is a convex function of xi is an element of R-N, rather than a function of the norm vertical bar xi vertical bar. The problem is formulated appropriately in an anisotropic Orlicz-Sobolev space associated with Phi. We study the existence of solutions and some other properties of the above problem and its corresponding variational inequality in such space.