Hamilton–Jacobi semigroup on length spaces and applications
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ané, 2000, Sur les inégalités de Sobolev logarithmiques, vol. 10
Bobkov, 2001, Hypercontractivity of Hamilton–Jacobi equations, J. Math. Pures Appl., 80, 669, 10.1016/S0021-7824(01)01208-9
Bobkov, 1999, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Funct. Anal., 163, 1, 10.1006/jfan.1998.3326
Burago, 2001, A Course in Metric Geometry, vol. 33
Cannarsa, 2004, Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control, vol. 58
Cheeger, 1999, Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal., 9, 428, 10.1007/s000390050094
Kuwai, 2001, Sobolev spaces, Laplacian, and heat kernel on Alexandrov spaces, Math. Z., 238, 269, 10.1007/s002090100252
Ledoux, 1999, Concentration of measure and logarithmic Sobolev inequalities, vol. 1709, 120
Ledoux, 2001
Lott
Lott
Otto, 2000, Generalization of an inequality by Talagrand, and links with the logarithmic Sobolev inequality, J. Funct. Anal., 173, 361, 10.1006/jfan.1999.3557
G. Perelman, A. Petrunin, Quasigeodesics and gradient curves in Alexandrov spaces, unpublished preprint
von Renesse
Sturm, 2006, On the geometry of metric measure spaces I, Acta Math., 196, 65, 10.1007/s11511-006-0002-8
Sturm, 2006, On the geometry of metric measure spaces II, Acta Math., 196, 133, 10.1007/s11511-006-0003-7
Villani, 2003, Topics in Optimal Transportation, vol. 58
C. Villani, Optimal transport, old and new, in preparation