Limits for Monge-Kantorovich mass transport problems
In this paper we study the limit of Monge-Kantorovich mass transfer problems when the involved measures are supported in a small strip near the boundary of a bounded smooth domain, Ω. Given two absolutely continues measures (with respect to the surface measure) supported on the boundary ∂Ω, by perfo...
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| Autores principales: | , , , |
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| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15340392_v7_n4_p853_Azorero |
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| Sumario: | In this paper we study the limit of Monge-Kantorovich mass transfer problems when the involved measures are supported in a small strip near the boundary of a bounded smooth domain, Ω. Given two absolutely continues measures (with respect to the surface measure) supported on the boundary ∂Ω, by performing a suitable extension of the measures to a strip of width ε near the boundary of the domain Ω we consider the mass transfer problem for the extensions. Then we study the limit as ε goes to zero of the Kantorovich potentials for the extensions and obtain that it coincides with a solution of the original mass transfer problem. Moreover we look for the possible approximations of these problems by solutions to equations involving the p-Laplacian for large values of p. |
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