Characterization of absolutely continuous curves in Wasserstein spaces

Calculus of Variations and Partial Differential Equations

Volumn 28, Issue 1, 2007, Pages 85-120

  Lisini, Stefano ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

[No Author keywords available]

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EID: 35348914033     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-006-0032-2     Document Type: Article

References (33)

1. Ambrosio, L.: Minimizing movements. Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. 19(5), 191-246 (1995)
2. Ambrosio, L.: Transport equation and Cauchy problem for BV vector fields. Invent. Math. 158(2), 227-260 (2004)
3. Ambrosio, L.: Transport equation and cauchy problem for non-smooth vector fields. Lecture Notes of the CIME Summer school in Cetrary, June 27-July 2, 2005, Available on line at http://cvgmt.sns.it/people/ambrosio/
4. Ambrosio, L., Kirchheim, B.: Rectifiable sets in metric and Banach spaces. Math. Ann. 318(3), 527-555 (2000)
5. Ambrosio, L., Tilli, P.: Topics on analysis in metric spaces, volume 25 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford (2004)
6. Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows in metric spaces and in the Wasserstein spaces of probability measures. Birkhäuser (2005)
7. Ambrosio, L., Lisini, S., Savaré, G.: Stability of flows associated to gradient vector fields and convergence of iterated transport maps. Preprint IMATI-CNR N.25-PV (2005)
8. Benamou, J.-D., Brenier,Y.:Acomputational fluidmechanics solution to theMonge-Kantorovich mass transfer problem. Numer. Math. 84(3), 375-393 (2000)
9. Bourbaki, N.: Éléments de mathématique. I: Les structures fondamentales de l'analyse. Fascicule VIII. Livre III: Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale. Deuxiéme édition revue et augmentée. Actualités Scientifiques et Industrielles, No. 1045. Hermann, Paris (1958)
10. Brancolini, Buttazzo, Santambrogio.: Path functionals over wasserstein spaces. Available on http://cvgmt.sns.it, 2005
11. Brézis, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Publishing Co., Amsterdam, 1973. North-Holland Mathematics Studies, No. 5. Notas de Matemática (50)
12. Brezis, H.: Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Maîtrise. [Collection of Applied Mathematics for the Master's Degree]. Masson, Paris, 1983. Théorie et applications. (Theory and applications)
13. Castaing, C., Valadier, M.: Convex analysis and measurable multifunctions. Springer, Berlin Heidelberg New York. Lecture Notes in Mathematics, Vol. 580 (1977)
14. Cordero-Erausquin, D., McCann, R.J., Schmuckenschläger, M.: A Riemannian interpolation inequality à la Borell, Brascamp and Lieb. Invent. Math. 146(2), 219-257 (2001)
15. Diestel, J., Uhl, J.J. Jr.: Vector measures. American Mathematical Society, Providence, R.I. With a foreword by B. J. Pettis, Mathematical Surveys, No. 15 (1977)
16. Feyel,D., Üstünel, A.:Measure transport onWiener space and the Girsanov theorem. C. R. Math. Acad. Sci. Paris 334(11), 1025-1028 (2002)
17. Feyel,D., Üstünel, A.S.:Monge-Kantorovitch measure transportation and Monge-Ampére equation on Wiener space. Probab. Theory Rela. Fields 128(3), 347-385 (2004)
18. Figiel, T., Wojtaszczyk, P.: Special bases in function spaces. In: Handbook of the geometry of Banach spaces, vol. I, pp. 561-597. North-Holland, Amsterdam (2001)
19. Jordan, R., Kinderlehrer,D.,Otto, F.: The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29(1), 1-17 (electronic) (1998)
20. Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces. I. Springer, Berlin Heidelberg New York. Sequence spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol. 92 (1977)
21. Lott, J., Villani, C.: Ricci curvature for metric-measure spaces via optimal transport. To appear. preprint available at http://www.umpa.ens-lyon.fr/ cvillani/Cedrif/pre.LV-Ricci.pdf, 2005
22. Lott, J., Villani, C.: Weak curvature conditions and poincaré inequalities. To appear. preprint available at http://www.umpa.ens-lyon.fr/ cvillani/Cedrif/, 2005
23. McCann, R.J.: A convexity principle for interacting gases. Adv. Math. 128(1), 153-179 (1997)
24. Otto, F.: The geometry of dissipative evolution equations: the porous medium equation. Comm. Partial Differ. Equ. 26(1-2), 101-174 (2001)
25. Otto, F., Villani, C.: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality. J. Funct. Anal. 173(2), 361-400 (2000)
26. von Renesse, M.-K., Sturm, K.-T.: Transport inequalities, gradient estimates, entropy, and Ricci curvature. Comm. Pure Appl. Math. 58(7), 923-940 (2005)
27. Rossi, R., Savaré, G.: Tightness, integral equicontinuity and compactness for evolution problems in Banach spaces. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 2(2), 395-431 (2003)
28. Schwartz, L.:Radon measures on arbitrary topological spaces and cylindricalmeasures. Published for the Tata Institute of Fundamental Research, Bombay by Oxford University Press, London. Tata Institute of Fundamental Research Studies in Mathematics, No. 6 (1973)
29. Sturm, K.-T.: Convex functionals of probability measures and nonlinear diffusions on manifolds. J. Math. Pures Appl. (9), 84(2), 149-168 (2005)
30. Sturm, K.T.: On the geometry of metric measure spaces. To appear. preprint available at http://www-wt.iam.uni-bonn.de/ sturm/en/index.html, 2005
31. Sturm, K.T.: On the geometry of metric measure spaces ii. To appear. preprint available at http://www-wt.iam.uni-bonn.de/ sturm/en/index.html, 2005
32. Villani, C.: Topics in optimal transportation, volume 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2003)
33. Westdickenberg, M., Otto, F.: Eulerian calculus for the contraction in the wasserstein distance. SIAM J. Math. Anal. (2005) (accepted)