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A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation

Autor
Caffarelli, L.; Gonzalez, M.; Nguyen, Truyen
Tipus d'activitat
Article en revista
Revista
Archive for rational mechanics and analysis
Data de publicació
2014-05-01
Volum
212
Número
2
Pàgina inicial
359
Pàgina final
414
DOI
https://doi.org/10.1007/s00205-013-0709-6 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repositori
http://hdl.handle.net/2117/22385 Obrir en finestra nova
Resum
We prove some interior regularity results for potential functions of optimal transportation problems with power costs. The main point is that our problem is equivalent to a new optimal transportation problem whose cost function is a sufficiently small perturbation of the quadratic cost, but it does not satisfy the well known condition (A.3) guaranteeing regularity. The proof consists in a perturbation argument from the standard Monge–Ampère equation in order to obtain, first, interior C1,1 es...
Citació
Caffarelli, L.; Gonzalez, M.; Nguyen, Truyen. A Perturbation argument for a Monge–Ampère type equation arising in optimal transportation. "Archive for rational mechanics and analysis", 01 Maig 2014, vol. 212, núm. 2, p. 359-414.
Paraules clau
AMPERE TYPE EQUATIONS, BOUNDARY-REGULARITY, CONTINUITY, CONVEX POTENTIALS, COST, INTERIOR, OPTIMAL MAPS, POTENTIAL FUNCTIONS, REARRANGEMENT, STRICT CONVEXITY
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants