On a comparison principle for Trudinger's equation

We study the comparison principle for non-negative solutions of the equation $\frac{\partial\,(|v|^{p-2}v)}{\partial t}\,=\, \textrm{div} (|\nabla v|^{p-2}\nabla v), \quad 1<p<\infty.$ 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.

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