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...
Guardado en:
| Autor principal: | |
|---|---|
| Publicado: |
2008
|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15340392_v7_n4_p853_Azorero http://hdl.handle.net/20.500.12110/paper_15340392_v7_n4_p853_Azorero |
| Aporte de: |
| 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. |
|---|