國立虎尾科技大學 |

The Monge-Ampère Equation

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The Monge-Ampère Equation/ by Cristian E. Gutiérrez.
Author:	Gutiérrez, Cristian E.
Description:	XIV, 216 p. 6 illus., 3 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Partial differential equations. -
Online resource:	https://doi.org/10.1007/978-3-319-43374-5
ISBN:	9783319433745

The Monge-Ampère Equation
Gutiérrez, Cristian E.

The Monge-Ampère Equation[electronic resource] /by Cristian E. Gutiérrez. - 2nd ed. 2016. - XIV, 216 p. 6 illus., 3 illus. in color.online resource. - Progress in Nonlinear Differential Equations and Their Applications,891421-1750 ;. - Progress in Nonlinear Differential Equations and Their Applications,87.

Generalized Solutions to Monge-Ampère Equations -- Uniformly Elliptic Equations in Nondivergence Form -- The Cross-sections of Monge-Ampère -- Convex Solutions of detDu=1 in R<i>n -- Regularity Theory for the Monge-Ampère Equation -- W^2,p Estimates for the Monge-Ampère Equation -- The Linearized Monge-Ampère Equation -- Interior Hölder Estimates for Second Derivatives -- References -- Index.

Now in its second edition, this monograph explores the Monge-Ampère 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-Ampère equation and a chapter on interior Hölder 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-Ampère-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:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

The Monge-Ampère Equation
LDR:03162nam a22004095i 4500 001 974976
003 DE-He213
005 20200707023931.0
007 cr nn 008mamaa
008 201211s2016 gw | s |||| 0|eng d
020 $a 9783319433745 $9 978-3-319-43374-5
024 7 $a 10.1007/978-3-319-43374-5 $2 doi
035 $a 978-3-319-43374-5
050 4 $a QA370-380
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
100 1 $a Gutiérrez, Cristian E. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1269610
245 1 4 $a The Monge-Ampère Equation $h [electronic resource] / $c by Cristian E. Gutiérrez.
250 $a 2nd ed. 2016.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2016.
300 $a XIV, 216 p. 6 illus., 3 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Progress in Nonlinear Differential Equations and Their Applications, $x 1421-1750 ; $v 89
505 0 $a Generalized Solutions to Monge-Ampère Equations -- Uniformly Elliptic Equations in Nondivergence Form -- The Cross-sections of Monge-Ampère -- Convex Solutions of detDu=1 in R<i>n -- Regularity Theory for the Monge-Ampère Equation -- W^2,p Estimates for the Monge-Ampère Equation -- The Linearized Monge-Ampère Equation -- Interior Hölder Estimates for Second Derivatives -- References -- Index.
520 $a Now in its second edition, this monograph explores the Monge-Ampère 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-Ampère equation and a chapter on interior Hölder 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-Ampère-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.
650 0 $a Partial differential equations. $3 1102982
650 0 $a Differential geometry. $3 882213
650 0 $a Mathematical physics. $3 527831
650 1 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783319433721
776 0 8 $i Printed edition: $z 9783319433738
776 0 8 $i Printed edition: $z 9783319828060
830 0 $a Progress in Nonlinear Differential Equations and Their Applications, $x 1421-1750 ; $v 87 $3 1264246
856 4 0 $u https://doi.org/10.1007/978-3-319-43374-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)