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

Abstract

We give a proof of Hölder continuity for bounded local weak solutions to the equation(∗) ut =XNi=1(|uxi|pi−2uxi)xi, in ΩT = Ω × (0, T], with Ω ⊂⊂ RN ,under the condition 2 < pi < p¯(1 + 2/N) for each i = 1, .., N, being p¯ the harmonic mean of the pis, via recentlydiscovered intrinsic Harnack estimates. Moreover, we establish an equivalent formulation of these Harnack estimateswithin the proper intrinsic geometry.Keywords: Anisotropic p-Laplacian, Hölder continuity, Harnack estimates, intrinsic scaling.