A NOTE ON THE POINT-WISE BEHAVIOUR OF BOUNDED SOLUTIONS FOR A NON-STANDARD ELLIPTIC OPERATOR

In this brief note we discuss local Holder continuity for solutions to anisotropic elliptic equations of the typeSigma(s)(i=1) partial derivative(ii)u + Sigma(N)(i=s+1) partial derivative(i) (A(i)(x, u, del u) = 0, x is an element of Omega subset of subset of R-N for 1 <= s <= N-1,where each operator A(i) behaves directionally as the singular p-Laplacian, 1 < p < 2 and the supercritical condition p + (N-s)(p-2) > 0 holds true. We show that the Harnack inequality can be proved without the continuity of solutions and that in turn this implies Holder continuity of solutions.