Covers the applications addressed and theoretical advances presented at a NSF-CBMS conference held at Florida Atlantic University (Boca Raton). This comprehensive volume outlines the directions in nonlinear analysis and its applications.

In recent years, the Monge Ampere 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.