On Hölder continuity and equivalent formulation of intrinsic Harnack estimates for an anisotropic parabolic degenerate prototype equation

We give a proof of Holder continuity for bounded local weak solutions to the equation(& lowast;) u(t) = Sigma(N)(i=1)(|u(xi)|(p)(i)-2u(xi))(xi) , in Omega(T) = Omega x (0, T], with Omega subset of subset of R-N,under the condition 2 < p(i) < p(1 + 2/N) for each i = 1, .., N, being p the harmonic mean of the p(i)s, via recently discovered intrinsic Harnack estimates. Moreover, we establish an equivalent formulation of these Harnack estimates within the proper intrinsic geometry.