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arXiv · 1901.03591

On a comparison principle for Trudinger's equation

Erik Lindgren·Peter Lindqvist
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Abstract

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 Poincar\'e inequalities in Sobolev spaces. We apply our result to obtain pointwise control of the large time behavior of solutions.

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Erik Lindgren, Peter Lindqvist. 2019-01-11. On a comparison principle for Trudinger's equation. https://arxiv.org/abs/1901.03591

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