Limits for Monge-Kantorovich mass transport problems

• Autores: Azorero, J.G.; Manfredi, J.J.; Peral, I.; Rossi, J.D.
• Año de publicación: 2008
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Commun. Pure Appl. Anal. 2008;7(4):853-865
• Materia: Mass transport; Neumann boundary conditions; Quasilinear elliptic equations
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

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.