A note on the point-wise behaviour of bounded solutions for a non-standard elliptic operator

In this brief note we discuss local Hölder continuity for solutions to anisotropic elliptic equations where each operator behaves directionally as the singular p-Laplacian, and the supercritical condition holds true. We show that the Harnack inequality can be proved without the continuity of solutions and that in turn this implies Hölder continuity of solutions.