東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Sobolev maps to the circle = from th...

Brezis, H.

Linked to FindBook

Google Book

Amazon

博客來

Sobolev maps to the circle = from the perspective of analysis, geometry, and topology /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Sobolev maps to the circle/ by Haim Brezis, Petru Mironescu.
Reminder of title:	from the perspective of analysis, geometry, and topology /
Author:	Brezis, H.
other author:	Mironescu, Petru.
Published:	New York, NY :Springer US : : 2021.,
Description:	xxxi, 530 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Sobolev spaces. -
Online resource:	https://doi.org/10.1007/978-1-0716-1512-6
ISBN:	9781071615126

Sobolev maps to the circle = from the perspective of analysis, geometry, and topology /
Brezis, H.

Sobolev maps to the circlefrom the perspective of analysis, geometry, and topology /[electronic resource] :by Haim Brezis, Petru Mironescu. - New York, NY :Springer US :2021. - xxxi, 530 p. :ill. (some col.), digital ;24 cm. - Progress in nonlinear differential equations and their applications,v. 962374-0280 ;. - Progress in nonlinear differential equations and their applications ;v. 96..

The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The "Complements and Open Problems" sections provide short introductions to various subsequent developments or related topics, and suggest new directions of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.

ISBN: 9781071615126

Standard No.: 10.1007/978-1-0716-1512-6doiSubjects--Topical Terms:

560929
Sobolev spaces.

LC Class. No.: QA323 / .B7 2021

Dewey Class. No.: 515.782

Sobolev maps to the circle = from the perspective of analysis, geometry, and topology /
LDR:02911nmm a2200337 a 4500 001 2301625
003 DE-He213
005 20220114192227.0
006 m d
007 cr nn 008maaau
008 230409s2021 nyu s 0 eng d
020 $a 9781071615126 $q (electronic bk.)
020 $a 9781071615102 $q (paper)
024 7 $a 10.1007/978-1-0716-1512-6 $2 doi
035 $a 978-1-0716-1512-6
035 $a 2301625
040 $a GP $c GP
041 0 $a eng
050 4 $a QA323 $b .B7 2021
072 7 $a PBKJ $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.782 $2 23
090 $a QA323 $b .B848 2021
100 1 $a Brezis, H. $3 3601212
245 1 0 $a Sobolev maps to the circle $h [electronic resource] : $b from the perspective of analysis, geometry, and topology / $c by Haim Brezis, Petru Mironescu.
260 $a New York, NY : $b Springer US : $b Imprint: Birkhauser, $c 2021.
300 $a xxxi, 530 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Progress in nonlinear differential equations and their applications, $x 2374-0280 ; $v v. 96
520 $a The theory of real-valued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifold-valued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the Monge-Kantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and non-local functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of sphere-valued Sobolev maps. Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The "Complements and Open Problems" sections provide short introductions to various subsequent developments or related topics, and suggest new directions of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena. Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the Ginzburg-Landau theory of superconductors.
650 0 $a Sobolev spaces. $3 560929
650 1 4 $a Differential Equations. $3 907890
650 2 4 $a Measure and Integration. $3 891263
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 891107
650 2 4 $a Algebraic Topology. $3 891269
700 1 $a Mironescu, Petru. $3 3601213
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Progress in nonlinear differential equations and their applications ; $v v. 96. $3 3601214
856 4 0 $u https://doi.org/10.1007/978-1-0716-1512-6
950 $a Mathematics and Statistics (SpringerNature-11649)