Limit for the p-laplacian equation with dynamical boundary conditions

Öztürk E., Rossi J. D.

Electronic Journal of Differential Equations, vol.01, no.Special Issue 01, pp.135-147, 2021 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 01 Issue: Special Issue 01
  • Publication Date: 2021
  • Journal Name: Electronic Journal of Differential Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.135-147
  • Hacettepe University Affiliated: Yes

Abstract

In this article we study the limit as p → ∞ 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.