2000 character limit reached
On a comparison principle for Trudinger's equation (1901.03591v2)
Published 11 Jan 2019 in math.AP
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.