A MASS-TRANSPORTATION APPROACH TO SHARP SOBOLEV AND GAGLIARDO-NIRENBERG INEQUALITIES

[1]  G. Burton TOPICS IN OPTIMAL TRANSPORTATION (Graduate Studies in Mathematics 58) By CÉDRIC VILLANI: 370 pp., US$59.00, ISBN 0-8218-3312-X (American Mathematical Society, Providence, RI, 2003) , 2004 .

[2]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[3]  C. Villani Topics in Optimal Transportation , 2003 .

[4]  Manuel del Pino,et al.  The optimal Euclidean Lp-Sobolev logarithmic inequality , 2003 .

[5]  Christian Houdré,et al.  Inequalities for generalized entropy and optimal transportation , 2003 .

[6]  Manuel del Pino,et al.  Nonlinear diffusions, hypercontractivity and the optimal LP-Euclidean logarithmic Sobolev inequality , 2004 .

[7]  Olivier Druet,et al.  The Ab Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems , 2002 .

[8]  Manuel del Pino,et al.  Best constants for Gagliardo–Nirenberg inequalities and applications to nonlinear diffusions☆ , 2002 .

[9]  V. V. Buldygin,et al.  Brunn-Minkowski inequality , 2000 .

[10]  Dario Cordero-Erausquin,et al.  Some Applications of Mass Transport to Gaussian-Type Inequalities , 2002 .

[11]  Gaoyong Zhang The affine Sobolev inequality , 1999 .

[12]  Olivier Druet,et al.  Best constants in Sobolev inequalities , 1998 .

[13]  F. Barthe On a reverse form of the Brascamp-Lieb inequality , 1997, math/9705210.

[14]  R. McCann A Convexity Principle for Interacting Gases , 1997 .

[15]  Pierre-Louis Lions,et al.  Convex symmetrization and applications , 1997 .

[16]  L. Caffarelli Boundary regularity of maps with convex potentials – II , 1996 .

[17]  R. McCann Existence and uniqueness of monotone measure-preserving maps , 1995 .

[18]  William Beckner,et al.  Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality , 1993 .

[19]  R. Schneider Convex Bodies: The Brunn–Minkowski Theory: Minkowski addition , 1993 .

[20]  L. Caffarelli Boundary regularity of maps with convex potentials , 1992 .

[21]  L. Evans Measure theory and fine properties of functions , 1992 .

[22]  L. Caffarelli The regularity of mappings with a convex potential , 1992 .

[23]  Y. Brenier Polar Factorization and Monotone Rearrangement of Vector-Valued Functions , 1991 .

[24]  E. Carlen,et al.  Extremals of functionals with competing symmetries , 1990 .

[25]  William P. Ziemer,et al.  Minimal rearrangements of Sobolev functions. , 1987 .

[26]  V. Milman,et al.  Asymptotic Theory Of Finite Dimensional Normed Spaces , 1986 .

[27]  Elliott H. Lieb,et al.  Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities , 1983 .

[28]  R. Osserman The isoperimetric inequality , 1978 .

[29]  G. Talenti,et al.  Best constant in Sobolev inequality , 1976 .

[30]  T. Aubin,et al.  Problèmes isopérimétriques et espaces de Sobolev , 1976 .

[31]  H. Knothe Contributions to the theory of convex bodies. , 1957 .