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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Autor principal: Rossi, Julio Daniel
Publicado: 2008
Materias:
Mass transport
Neumann boundary conditions
Quasilinear elliptic equations
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
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15340392_v7_n4_p853_Azorero
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spelling paper:paper_15340392_v7_n4_p853_Azorero2023-06-08T16:20:01Z Limits for Monge-Kantorovich mass transport problems Rossi, Julio Daniel Mass transport Neumann boundary conditions Quasilinear elliptic equations 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. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Mass transport
Neumann boundary conditions
Quasilinear elliptic equations
spellingShingle Mass transport
Neumann boundary conditions
Quasilinear elliptic equations
Rossi, Julio Daniel
Limits for Monge-Kantorovich mass transport problems
topic_facet Mass transport
Neumann boundary conditions
Quasilinear elliptic equations
description 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.
author Rossi, Julio Daniel
author_facet Rossi, Julio Daniel
author_sort Rossi, Julio Daniel
title Limits for Monge-Kantorovich mass transport problems
title_short Limits for Monge-Kantorovich mass transport problems
title_full Limits for Monge-Kantorovich mass transport problems
title_fullStr Limits for Monge-Kantorovich mass transport problems
title_full_unstemmed Limits for Monge-Kantorovich mass transport problems
title_sort limits for monge-kantorovich mass transport problems
publishDate 2008
url 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
work_keys_str_mv AT rossijuliodaniel limitsformongekantorovichmasstransportproblems
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