Mario Milman

Jie Xiao

Boguslaw Zegarlinski

This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.

Geometric Potential Analysis

Luis A. Caffarelli

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.

Applications to Geometry and Optimization : NSF-CBMS Conference on the Monge Ampère Equation, Applications to Geometry and Optimization, July 9-13, 1997, Florida Atlantic University

Mario Milman

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