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.
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Ireneo Peral, Jesús García-Azorero, Juan J. Manfredi, Julio D. Rossi, 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. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 2, pp. 111–126DOI 10.4171/RLM/536