Topological Methods in Nonlinear Analysis

Mixed boundary condition for the Monge-Kantorovich equation

Noureddne Igbida, Stanislas Ouaro, and Urbain Tradore

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Abstract

In this work we give some equivalent formulations for the optimization problem \begin{multline*} \max\bigg\{ \int_{\Omega} \xi \,d\mu + \int_{\Gamma_{N}}\xi \,d\nu;\ \xi \in W^{1,\infty}(\Omega) \text{ such that } \\ \xi_{/\Gamma_{D}}= 0,\ |\nabla\xi(x)|\leq 1 \text{ a.e. } x\in \Omega\bigg\}, \end{multline*} where the boundary of $\Omega$ is $\Gamma=\Gamma_{N}\cup\Gamma_{D}$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 1 (2016), 109-123.

Dates
First available in Project Euclid: 23 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1458740732

Digital Object Identifier
doi:10.12775/TMNA.2015.088

Mathematical Reviews number (MathSciNet)
MR3469050

Zentralblatt MATH identifier
1373.49013

Citation

Igbida, Noureddne; Ouaro, Stanislas; Tradore, Urbain. Mixed boundary condition for the Monge-Kantorovich equation. Topol. Methods Nonlinear Anal. 47 (2016), no. 1, 109--123. doi:10.12775/TMNA.2015.088. https://projecteuclid.org/euclid.tmna/1458740732


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