Symmetry and monotonicity results for solutions of vectorial p-stokes systems

Abstract

In this paper we shall study qualitative properties of a p-Stokes type system, namely -Delta pu = - div(|Du|p-2Du) = f (x, u) in omega, where Delta p is the p-Laplacian vectorial operator. More precisely, under suitable assumptions on the domain omega and the function f, it is deduced that system solutions are symmetric and monotone. Our main results are derived from a vectorial version of the weak and strong comparison principles, which enable to proceed with the moving-planes technique for systems. As far as we know, these are the first qualitative kind results involving vectorial operators.