On Hölder continuity-in-time of the optimal transport map towards measures along a curve

Proceedings of the Edinburgh Mathematical Society

Volumn 54, Issue 2, 2011, Pages 401-409

  Gigli, Nicola ^a,b  

^a UNIVERSITÉ DE BORDEAUX   (France)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

H lder continuity; optimal transport; regularity in time

Indexed keywords

EID: 79956158612     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/S001309150800117X     Document Type: Article

References (9)

1. L. Ambrosio, N. Gigli and G. Savaŕe, Gradient flows in metric spaces and in the space of probability measures (Birkhäuser, Basel, 2005).
2. Y. Brenier, Polar factorization and monotone rearrangement of vector-valued functions, Commun. Pure Appl. Math. 44 (1991), 375-417.
3. L. A. Caffarelli, The regularity of mappings with a convex potential, J. Am. Math. Soc. 5 (1992), 99-104.
4. L. A. Caffarelli, Boundary regularity of maps with convex potentials, Commun. Pure Appl. Math. 45 (1992), 1141-1151.
5. L. A. Caffarelli, Boundary regularity of maps with convex potentials, II, Annals Math. (2) 144 (1996), 453-496. (Pubitemid 126345436)
6. N. Gigli, On the geometry of the space of measures in Rd endowed with the quadratic optimal transportation distance, PhD thesis, Scuola Normale Superiore, Pisa (2008; available at http://cvgmt.sns.it/people/gigli/).
7. G. Loeper, On the regularity of the polar factorization for time dependent maps, Calc. Var. PDEs 22 (2005), 343-374. (Pubitemid 40180156)
8. F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Commun. PDEs 26 (2001), pp. 101-174. (Pubitemid 33731270)
9. C. Villani, Optimal transport, old and new (Springer, 2008).