MARC details
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02374nam a22001937a 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20241004154929.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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241004b |||||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781071615102 |
| 100 ## - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Brezis, Haim |
| 245 ## - TITLE STATEMENT |
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| Title |
Sobolev Maps to the Circle: |
| Remainder of title |
From the perspective of analysis, geometry and topology/ |
| Statement of responsibility, etc. |
Haim Brezis |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. |
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| Name of publisher, distributor, etc. |
Springer Nature, |
| Date of publication, distribution, etc. |
2021. |
| 300 ## - Physical Description |
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| Pages: |
xxxi,530 p. |
| 490 ## - SERIES STATEMENT |
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| Series statement |
Progress in Nonlinear Differential Equations and their applications 96 |
| 500 ## - GENERAL NOTE |
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| General note |
PNLDE 96 |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
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. <br/><br/>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<br/>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.<br/><br/><br/>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.<br/> |
| 700 ## - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Mironescu, Petru |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
| Edition |
23rd ed. |
| Call number prefix |
BREZ |
| Call number suffix |
515 |
