Local regularity for solutions to quasi-linear singular parabolic equations with anisotropic weights

Abstract

This paper develops a concise procedure for the study on local behavior of solutions to anisotropically weighted quasi-linear singular parabolic equations of $p$-Laplacian type, which is realized by improving the energy inequalities and applying intrinsic scaling factor to the De Giorgi truncation method. In particular, it also presents a new proof for local Hölder continuity of the solution in the unweighted case.

arXiv commentWe achieve a concise and elegant proof by improving the energy inequalities and applying the redefined intrinsic scaling factor to the De Giorgi truncation method