In recent years, the Monge Ampère 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.

Readership

Graduate students, research and applied mathematicians working in nonlinear analysis; also physicists, engineers and meteorologists.

Table of Contents

• J.-D. Benamou and Y. Brenier -- A numerical method for the optimal time-continuous mass transport problem and related problems
• L. A. Caffarelli, S. A. Kochengin, and V. I. Oliker -- On the numerical solution of the problem of reflector design with given far-field scattering data
• M. J. P. Cullen and R. J. Douglas -- Applications of the Monge-Ampére equation and Monge transport problem to meterology and oceanography
• M. Feldman -- Growth of a sandpile around an obstacle
• W. Gangbo -- The Monge mass transfer problem and its applications
• B. Guan -- Gradient estimates for solutions of nonparametric curvature evolution with prescribed contact angle condition
• L. G. Hanin -- An extension of the Kantorovich norm
• M. McAsey and L. Mou -- Optimal locations and the mass transport problem
• E. Newman and L. P. Cook -- A generalized Monge-Ampére equation arising in compressible flow
• J. Urbas -- Self-similar solutions of Gauss curvature flows