JournalsrlmVol. 20 , No. 2DOI 10.4171/rlm/536

The limit as <var>p</var> → ∞ for the <em>p</em>-Laplacian with mixed boundary conditions and the mass transport problem through a given window

  • Ireneo Peral

    Universidad Autónoma de Madrid, Spain
  • Jesús García-Azorero

    Universidad Autónoma de Madrid, Spain
  • Juan J. Manfredi

    University of Pittsburgh, United States
  • Julio D. Rossi

    Universidad de Buenos Aires, Argentina
The limit as <var>p</var> → ∞ for the <em>p</em>-Laplacian with mixed boundary conditions and the mass transport problem through a given window cover

Abstract

In this paper we study the limit as p → ∞ in a PDE problem involving the p-Laplacian with a right hand side, − div(|Du|p − 2Du) = f, with mixed boundary conditions, u = 0 on Γ and |Du|p − 2 ∂u⁄∂ν = 0 on ∂Ω \ Γ. We find that this limit is related to an optimal mass transport problem, where the total mass given by f is transported outside the domain through a given window on the boundary Γ.