ON A GLOBAL GRADIENT ESTIMATE IN p-LAPLACIAN PROBLEMS

We make explicit the p-dependence of C in the gradient estimate parallel to del u parallel to(p-1 )(infinity)<= C parallel to f parallel to(N,1) by Cianchi and Maz'ya (2011). In such inequality, the constant C is uniform with respect to f is an element of L-N,L-1(Omega), and u is the weak solution to the Poisson equation -div(|del u|(p-2)del u) = f in a bounded domain Omega subset of R-N, N >= 3, coupled with either Neumann or Dirichlet homogeneous boundary conditions. The case N = 2 with f is an element of L-q(Omega), for some q>2, is also considered .