Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Amp?re and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view.
The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris Subseries: Fondazione C.I.M.E., Firenze Adviser: Pietro Zecca
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3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo
L. Ambrosio G. Buttazzo
L. A. Caffarelli C. Villani
Y. Brenier
Optimal Transportation and Applications Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2--8, 2001 Editors: L. A. Caffarelli S. Salsa
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Authors and Editors Luigi Ambrosio Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italy e-mail:
[email protected] Luis A. Caffarelli Department of Mathematics University of Texas at Austin Austin, TX78712-1082, USA e-mail:
[email protected] Yann Brenier Laboratoire J. A. Dieudonn´e Universit´e de Nice-Sophia Antipolis Parc Valrose 06108 Nice, France e-mail:
[email protected]
Gius