Lawrence C. Evans

Luis A. Caffarelli

Luigi Ambrosio

Michael G. Crandall

Nicola Fusco

Centro internazionale matematico estivo. Summer School

E. Mascolo

With a historical overview by Elvira Mascolo

Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 27 - July 2, 2005

Calculus of Variations and Nonlinear Partial Differential Equations

Cédric Villani

Giuseppe Buttazzo

Yann Brenier

Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère 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.

Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 2–8, 2001

Optimal Transportation and Applications

Mario Milman

In recent years, the Monge Ampere Equation has received attention for its role in several new areas of applied mathematics: As a new method of discretization for evolution equations of classical mechanics, such as the Euler equation, flow in porous media, Hele-Shaw flow, etc., As a simple model for optimal transportation and a div-curl decomposition with affine invariance and As a model for front formation in meteorology and optimal antenna design. These applications were addressed and important theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). L. Cafarelli and other distinguished specialists contributed high-quality research results and up-to-date developments in the field. This is a comprehensive volume outlining current directions in nonlinear analysis and its applications.

Applications to Geometry and Optimization : NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University

Monge Ampère Equation

Luis A. Caffarelli

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