Guti?rrez The Monge-Amp?re Equation 9783319433721

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Автор: Guti?rrez
Название: The Monge-Amp?re Equation
ISBN: 9783319433721
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Дифференциальное исчисление и дифференциальные уравнения

Геометрия

ISBN-10: 3319433725
Обложка/Формат: Hardback
Страницы: 216
Вес: 0.50 кг.
Дата издания: 2016
Серия: Progress in Nonlinear Differential Equations and Their Applications
Язык: English
Издание: 2nd ed. 2016
Иллюстрации: 3 illustrations, color; 3 illustrations, black and white; xiv, 216 p. 6 illus., 3 illus. in color.
Размер: 165 x 292 x 19
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: Now in its second edition, this monograph explores the Monge-Amp?re equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Amp?re equation and a chapter on interior H?lder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Amp?re-type equations and their diverse applications in the areas of differential geometry, the calculus of variations, optimization problems, optimal mass transport, and geometric optics. Both researchers and graduate students working on nonlinear differential equations and their applications will find this to be a useful and concise resource.
Дополнительное описание: Generalized Solutions to Monge-Amp?re Equations.- Uniformly Elliptic Equations in Nondivergence Form.- The Cross-sections of Monge-Amp?re.- Convex Solutions of detD2u=1 in Rn.- Regularity Theory for the Monge-Amp?re Equation.- W^2,p Estimates for t

The Monge-Amp?re Equation, Guti?rrez