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The Monge-Ampere equation
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The Monge-Ampere equation
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/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. -
電子資源:
http://dx.doi.org/10.1007/978-3-319-43374-5
ISBN:
9783319433745
The Monge-Ampere equation
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:
890177
Monge-Ampere equations.
LC Class. No.: QA377
Dewey Class. No.: 515.353
The Monge-Ampere equation
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