Monge Ampère Equation: Applications to Geometry and Optimization
About this Title
Luis A. Caffarelli and Mario Milman, Editors
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.
Graduate students, research and applied mathematicians working in nonlinear analysis; also physicists, engineers and meteorologists.
Table of Contents
- Jean-David Benamou and Yann Brenier – A numerical method for the optimal time-continuous mass transport problem and related problems [MR 1660739]
- Luis A. Caffarelli, Sergey A. Kochengin and Vladimir I. Oliker – On the numerical solution of the problem of reflector design with given far-field scattering data [MR 1660740]
- M. J. P. Cullen and R. J. Douglas – Applications of the Monge-Ampère equation and Monge transport problem to meteorology and oceanography [MR 1660741]
- Mikhail Feldman – Growth of a sandpile around an obstacle [MR 1660742]
- Wilfrid Gangbo – The Monge mass transfer problem and its applications [MR 1660743]
- Bo Guan – Gradient estimates for solutions of nonparametric curvature evolution with prescribed contact angle condition [MR 1660744]
- Leonid G. Hanin – An extension of the Kantorovich norm [MR 1660745]
- Michael McAsey and Libin Mou – Optimal locations and the mass transport problem [MR 1660746]
- Elsa Newman and L. Pamela Cook – A generalized Monge-Ampère equation arising in compressible flow [MR 1660747]
- John Urbas – Self-similar solutions of Gauss curvature flows [MR 1660748]