The limit as $p → ∞$ for the $p$-Laplacian with mixed boundary conditions and the mass transport problem through a given window | Zendy

Jesús García-Azorero | Zendy; Juan J. Manfredi | Zendy; Ireneo Peral | Zendy; Julio D. Rossi | Zendy

Open Access

The limit as $p → ∞$ for the $p$-Laplacian with mixed boundary conditions and the mass transport problem through a given window

Author(s) -

Jesús García-Azorero,

Juan J. Manfredi,

Ireneo Peral,

Julio D. Rossi

Publication year - 2009

Publication title -

rendiconti lincei matematica e applicazioni

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.824

H-Index - 28

eISSN - 1720-0768

pISSN - 1120-6330

DOI - 10.4171/rlm/536

Subject(s) - mathematics , limit (mathematics) , window (computing) , laplace operator , p laplacian , boundary (topology) , mass transport , mathematical analysis , boundary value problem , physics , computer science , engineering physics , operating system

In this paper we study the limit as p → ∞ in a PDE problem involving the p−Laplacian with a right hand side, −div(|Du|Du) = f , with mixed boundary conditions, u = 0 on Γ and |Du| ∂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.

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