The Monge-Ampиre Equation, Gutiйrrez Cristian E.

Автор: Guti?rrez
Название: The Monge-Amp?re Equation
ISBN: 3319433725 ISBN-13(EAN): 9783319433721
Издательство: Springer
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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.

Автор: Cristian E. Gutierrez
Название: The Monge—Amp?re Equation
ISBN: 1461266564 ISBN-13(EAN): 9781461266563
Издательство: Springer
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Цена: 11179.00 р.
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Описание: The Monge-Ampere equation has attracted considerable interest in recent years because of its important role in several areas of applied mathematics.

Автор: Hiroyoshi Mitake; Hung V. Tran; Nam Q. Le; Hiroyos
Название: Dynamical and Geometric Aspects of Hamilton-Jacobi and Linearized Monge-Amp?re Equations
ISBN: 3319542079 ISBN-13(EAN): 9783319542072
Издательство: Springer
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Цена: 4890.00 р.
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Описание: Preface by Nguyen Huu Du (Managing director of VIASM).-Miroyoshi Mitake and Hung V. Tran: Dynamical properties of Hamilton-Jacobi equations via the nonlinear adjoint method: Large time behavior and Discounted approximation.- Nam Q. Le: The second boundary value problem of the prescribed affine mean curvature equation and related linearized Monge-Ampиre equation.