Local symmetry and non uniformly elliptic operators, in preparation

Abstract. The goal of this paper is to study the symmetry properties of nonnegative solutions of elliptic equations involving a non uniformly elliptic operator. We consider on a ball the solutions of pu + f(u) = 0 with zero Dirichlet boundary conditions, for p> 2, where p is the p-Laplace operator and f a continuous nonlinearity. The main tools are a comparison result for weak solutions and a local moving plane method which has been previously used in the p = 2 case. We prove local and global symmetry results when u is of class C 1; for large enough, under some additional technical assumptions