The limit as $p\rightarrow\infty$ for the $p$Laplacian equation with dynamical boundary conditions
Abstract
In this paper we study the limit as $p\to \infty$ in the evolution problem driven by the $p$Laplacian with dynamical boundary conditions. We prove that the natural energy functional associated with this problem converges to a limit in the sense of Mosco convergence and as a consequence we obtain convergence of the solutions to the evolution problems. For the limit problem we show an interpretation in terms of optimal mass transportation and provide examples of explicit solutions for some particular data.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.13128
 Bibcode:
 2021arXiv210813128O
 Keywords:

 Mathematics  Analysis of PDEs;
 35K20;
 35K55;
 35K92;
 47J35