The limit case in a nonlocal p -Laplacian equation with dynamical boundary conditions

• Eylem Öztürk ^[1]
  1. [1] Hacettepe University

     Hacettepe University

     Turquía

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 2, 2024, págs. 567-591
• Idioma: inglés
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• Resumen

  • In this paper we deal with the limit as p→∞ for the nonlocal analogous to the p-Laplacian evolution with dynamic boundary conditions. Our main result demonstrates this limit in both the elliptic and parabolic cases. We are interested in smooth and singular kernels and show the existence and uniqueness of a limit solution. We obtain that the limit solution of the elliptic problem turns out to be also a viscosity solution of a corresponding problem. We prove that the natural energy functionals associated with this problem converge, in the sense of Mosco, to a limit functional and therefore we obtain convergence of solutions to the evolution problems in the parabolic case. For the limit problem, we provide examples of explicit solutions for some particular data.