On a comparison principle for Trudinger's equation

Abstract

We study the comparison principle for non-negative solutions of the equation $$\frac{\partial (|v{|}^{p-2}v)}{\partial t}=\text{div}(|\nabla v{|}^{p-2}\nabla v),1<p<\infty .$$ This equation is related to extremals of Poincaré inequalities in Sobolev spaces. We apply our result to obtain pointwise control of the large time behavior of solutions.