Limits for Monge-Kantorovich mass transport problems

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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: Azorero, J.G., Manfredi, J.J., Peral, I., Rossi, J.D.
Formato: JOUR
Materias:
Mass transport
Neumann boundary conditions
Quasilinear elliptic equations
Acceso en línea: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 todo:paper_15340392_v7_n4_p853_Azorero
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spelling todo:paper_15340392_v7_n4_p853_Azorero2023-10-03T16:21:37Z Limits for Monge-Kantorovich mass transport problems Azorero, J.G. Manfredi, J.J. Peral, I. Rossi, J.D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Azorero, J.G.
Manfredi, J.J.
Peral, I.
Rossi, J.D.
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.
format JOUR
author Azorero, J.G.
Manfredi, J.J.
Peral, I.
Rossi, J.D.
author_facet Azorero, J.G.
Manfredi, J.J.
Peral, I.
Rossi, J.D.
author_sort Azorero, J.G.
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
url http://hdl.handle.net/20.500.12110/paper_15340392_v7_n4_p853_Azorero
work_keys_str_mv AT azorerojg limitsformongekantorovichmasstransportproblems
AT manfredijj limitsformongekantorovichmasstransportproblems
AT perali limitsformongekantorovichmasstransportproblems
AT rossijd limitsformongekantorovichmasstransportproblems
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