國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Sobolev maps to the circlefrom the p...

Brezis, H.

Sobolev maps to the circlefrom the perspective of analysis, geometry, and topology /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Sobolev maps to the circleby Haim Brezis, Petru Mironescu.
其他題名:	from the perspective of analysis, geometry, and topology /
作者:	Brezis, H.
其他作者:	Mironescu, Petru.
出版者:	New York, NY :Springer US :2021.
面頁冊數:	xxxi, 530 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Sobolev spaces.
電子資源:	https://doi.org/10.1007/978-1-0716-1512-6
ISBN:	9781071615126$q(electronic bk.)

Sobolev maps to the circlefrom 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.83..

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$q(electronic bk.)

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

247270
Sobolev spaces.

LC Class. No.: QA323 / .B7 2021

Dewey Class. No.: 515.782

Sobolev maps to the circlefrom the perspective of analysis, geometry, and topology /
LDR:02887nmm a2200325 a 4500 001 616101
003 DE-He213
005 20220114192227.0
006 m d
007 cr nn 008maaau
008 220831s2021 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
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. $q (Haim) $3 438751
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 247270
650 1 4 $a Differential Equations. $3 285983
650 2 4 $a Measure and Integration. $3 273777
650 2 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Algebraic Topology. $3 273784
700 1 $a Mironescu, Petru. $3 915045
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Progress in nonlinear differential equations and their applications ; $v v.83. $3 558793
856 4 0 $u https://doi.org/10.1007/978-1-0716-1512-6
950 $a Mathematics and Statistics (SpringerNature-11649)