Monge Ampère Equation: Applications to Geometry and Optimization
About this Volume
Edited by: Luis A. Caffarelli and Mario Milman
1999: Volume: 226
ISBNs: 978-0-8218-0917-4 (print); 978-0-8218-7817-0 (online)
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
- 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
- M. J. P. Cullen and R. J. Douglas – Applications of the Monge-Ampère equation and Monge transport problem to meteorology and oceanography
- Mikhail Feldman – Growth of a sandpile around an obstacle
- Wilfrid Gangbo – The Monge mass transfer problem and its applications
- Bo Guan – Gradient estimates for solutions of nonparametric curvature evolution with prescribed contact angle condition
- Leonid G. Hanin – An extension of the Kantorovich norm
- Michael McAsey and Libin Mou – Optimal locations and the mass transport problem
- Elsa Newman and L. Pamela Cook – A generalized Monge-Ampère equation arising in compressible flow
- John Urbas – Self-similar solutions of Gauss curvature flows