On Holder 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 $u_t= sum_{i=1}^N (|u_{x_i}|^{p_i-2} u_{x_i})_{x_i}$, in $Omega times [0,T]$, with $Omega subset subset mathbb{R}^N$, under the condition $ 2<p_i<bar{p}(1+2/N)$ for each $i=1,..,N$, being $bar{p}$ the harmonic mean of the $p_i$s, via recently discovered intrinsic Harnack estimates. Moreover we establish equivalent forms of these Harnack estimates within the proper intrinsic geometry.