Overdetermined Problems for Some Fully Non Linear Operators

In this paper, we consider the equation |delta u|M a, A (D 2 u)= f(u) in a bounded smooth domain , with both Dirichlet condition u=0 and Neumann condition , where c is a constant, > 1, u is of constant sign and M a, A is one of the Pucci operator. We prove, for different nonlinearities f, that, when a is sufficiently close to A, either u=c=0=f(0) or is a ball, u is radial, and c0 in .