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The Monge-Ampere equation[electronic...

Gutierrez, Cristian E.

The Monge-Ampere equation[electronic resource] /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.353
書名/作者:	The Monge-Ampere equation/ by Cristian E. Gutierrez.
作者:	Gutierrez, Cristian E.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	xiv, 216 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Monge-Ampere equations.
標題:	Mathematics.
標題:	Partial Differential Equations.
標題:	Differential Geometry.
標題:	Mathematical Applications in the Physical Sciences.
ISBN:	9783319433745
ISBN:	9783319433721
摘要、提要註:	Now in its second edition, this monograph explores the Monge-Ampere 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-Ampere equation and a chapter on interior Holder 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-Ampere-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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-43374-5

The Monge-Ampere equation[electronic resource] /
Gutierrez, Cristian E.

The Monge-Ampere equation[electronic resource] /by Cristian E. Gutierrez. - 2nd ed. - Cham :Springer International Publishing :2016. - xiv, 216 p. :ill., digital ;24 cm. - Progress in nonlinear differential equations and their applications,v.891421-1750 ;. - Progress in nonlinear differential equations and their applications ;v.83..

Now in its second edition, this monograph explores the Monge-Ampere 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-Ampere equation and a chapter on interior Holder 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-Ampere-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.

ISBN: 9783319433745

Standard No.: 10.1007/978-3-319-43374-5doiSubjects--Topical Terms:

467500
Monge-Ampere equations.

LC Class. No.: QA377

Dewey Class. No.: 515.353

The Monge-Ampere equation[electronic resource] /
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520 $a Now in its second edition, this monograph explores the Monge-Ampere 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-Ampere equation and a chapter on interior Holder 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-Ampere-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.
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