On Holder Continuity and Equivalent Formulation of Intrinsic Harnack Estimates for an Anisotropic Parabolic Degenerate Prototype Equation

We give a proof of H"older continuity for bounded local weak solutions to the equation $u_t={\sum }_{i=1}^N(\mathrm{\mid }{u}_{x_i}{\mathrm{\mid }}^{p_i-2}{u}_{x_i}{)}_{x_i}$, in $\Omega \times [0,T]$,with$\Omega \subset \subset $\mathbb{R}$^N$,underthecondition$ 2<p_i<\bar{p}(1+2/N)$foreach$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.