Qualitative properties of solutions to parabolic anisotropic equations: Part II. The anisotropic Trudinger's equation

Abstract

We study the local regularity properties of weak solutions to a special class of anisotropic doubly nonlinear parabolic operators, whose prototype is the anisotropic Trudinger's equation. We prove a parabolic Harnack inequality, valid without any restrictions on the exponents $p_i$s. When the range of diffusion exponents is restricted, solutions are Hölder continuous.