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Monge Ampère Equation: Applications to Geometry and Optimization
Edited by: Luis A. Caffarelli, New York University-Courant Institute of Mathematical Sciences, NY, and Mario Milman, Florida Atlantic University, Boca Raton, FL

Contemporary Mathematics
1999; 172 pp; softcover
Volume: 226
ISBN-10: 0-8218-0917-2
ISBN-13: 978-0-8218-0917-4
List Price: US$50
Member Price: US$40
Order Code: CONM/226
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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

  • 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
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