Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence
We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients b<inf>p</inf> that in particular verify that lim<inf>p→∞</inf> b<inf>p</inf>...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_21919496_v3_n3_p133_Mazon |
| Aporte de: |
| id |
todo:paper_21919496_v3_n3_p133_Mazon |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_21919496_v3_n3_p133_Mazon2023-10-03T16:40:18Z Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence Mazón, J.M. Rossi, J.D. Toledo, J. Mass transport Monge-Kantorovich problems P-Laplacian equation We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients b<inf>p</inf> that in particular verify that lim<inf>p→∞</inf> b<inf>p</inf> = b uniformly in Ω¯, we prove that there is a uniform limit of u<inf>pj</inf> (along a sequence pj →∞) and that this limit is a Kantorovich potential for the optimal mass transport problem of f<inf>+</inf> to f<inf>-</inf> with cost c(x, y) given by the formulac(x, y) = inf<inf>σ(0)=x,σ(1)=y</inf> f<inf>σ</inf>bds. 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_21919496_v3_n3_p133_Mazon |
| 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 Monge-Kantorovich problems P-Laplacian equation |
| spellingShingle |
Mass transport Monge-Kantorovich problems P-Laplacian equation Mazón, J.M. Rossi, J.D. Toledo, J. Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| topic_facet |
Mass transport Monge-Kantorovich problems P-Laplacian equation |
| description |
We consider the following problem: given a bounded convex domain ω ⊂ ℝN we consider the limit as p →∞ of solutions to (Equation Presented) Under appropriate assumptions on the coefficients b<inf>p</inf> that in particular verify that lim<inf>p→∞</inf> b<inf>p</inf> = b uniformly in Ω¯, we prove that there is a uniform limit of u<inf>pj</inf> (along a sequence pj →∞) and that this limit is a Kantorovich potential for the optimal mass transport problem of f<inf>+</inf> to f<inf>-</inf> with cost c(x, y) given by the formulac(x, y) = inf<inf>σ(0)=x,σ(1)=y</inf> f<inf>σ</inf>bds. |
| format |
JOUR |
| author |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_facet |
Mazón, J.M. Rossi, J.D. Toledo, J. |
| author_sort |
Mazón, J.M. |
| title |
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| title_short |
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| title_full |
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| title_fullStr |
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| title_full_unstemmed |
Mass transport problems obtained as limits of p-Laplacian type problems with spatial dependence |
| title_sort |
mass transport problems obtained as limits of p-laplacian type problems with spatial dependence |
| url |
http://hdl.handle.net/20.500.12110/paper_21919496_v3_n3_p133_Mazon |
| work_keys_str_mv |
AT mazonjm masstransportproblemsobtainedaslimitsofplaplaciantypeproblemswithspatialdependence AT rossijd masstransportproblemsobtainedaslimitsofplaplaciantypeproblemswithspatialdependence AT toledoj masstransportproblemsobtainedaslimitsofplaplaciantypeproblemswithspatialdependence |
| _version_ |
1807323078550618112 |