A new $L^\infty$ estimate in optimal mass transport
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- by G. Bouchitté, C. Jimenez and M. Rajesh PDF
- Proc. Amer. Math. Soc. 135 (2007), 3525-3535 Request permission
Abstract:
Let $\Omega$ be a bounded Lipschitz regular open subset of $\mathbb {R}^d$ and let $\mu ,\nu$ be two probablity measures on $\overline {\Omega }$. It is well known that if $\mu =f dx$ is absolutely continuous, then there exists, for every $p>1$, a unique transport map $T_p$ pushing forward $\mu$ on $\nu$ and which realizes the Monge-Kantorovich distance $W_p(\mu ,\nu )$. In this paper, we establish an $L^\infty$ bound for the displacement map $T_p x-x$ which depends only on $p$, on the shape of $\Omega$ and on the essential infimum of the density $f$.References
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Additional Information
- G. Bouchitté
- Affiliation: UFR Sciences, Université du Sud-Toulon-Var, BP20132, 83957 La Garde Cedex, France
- Email: bouchitte@univ-tln.fr
- C. Jimenez
- Affiliation: UFR Sciences, Université du Sud-Toulon-Var, BP20132, 83957 La Garde Cedex, France
- Email: c.jimenez@sns.it
- M. Rajesh
- Affiliation: Departemento de Matematica, Facultad de Ciencias Fisicas y Matematicas, Universidad de Concepcion, Casilla 160-C. Concepcion, Chile
- Email: rmahadevan@udec.cl
- Received by editor(s): January 9, 2006
- Received by editor(s) in revised form: June 23, 2006
- Published electronically: July 3, 2007
- Communicated by: David Preiss
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3525-3535
- MSC (2000): Primary 39B62, 46N10, 49Q20
- DOI: https://doi.org/10.1090/S0002-9939-07-08877-6
- MathSciNet review: 2336567