**Contemporary Mathematics**

Volume: 226;
1999;
172 pp;
Softcover

MSC: Primary 35; 46; 49; 58;

Print ISBN: 978-0-8218-0917-4

Product Code: CONM/226

List Price: $50.00

Individual Member Price: $40.00

**Electronic ISBN: 978-0-8218-7817-0
Product Code: CONM/226.E**

List Price: $50.00

Individual Member Price: $40.00

# Monge Ampère Equation: Applications to Geometry and Optimization

Share this page *Edited by *
*Luis A. Caffarelli; Mario Milman*

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.

#### Table of Contents

# Table of Contents

## Monge Ampere Equation: Applications to Geometry and Optimization

- Contents vii8 free
- Preface ix10 free
- A numerical method for the optimal time-continuous mass transport problem and related problems 112 free
- On the numerical solution of the problem of reflector design with given far-field scattering data 1324
- Applications of the Monge-Ampère equation and Monge transport problem to meteorology and oceanography 3344
- Growth of a sandpile around an obstacle 5566
- The Monge mass transfer problem and its applications 7990
- Gradient estimates for solutions of nonparametric curvature evolution with prescribed contact angle condition 105116
- An extension of the Kantorovich norm 113124
- Optimal locations and the mass transport problem 131142
- A generalized Monge-Ampère equation arising in compressible flow 149160
- Self-similar solutions of Gauss curvature flows 157168

#### Readership

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