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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.

atti della accademia nazionale dei lincei. rendiconti lincei. matematica e applicazioni

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