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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Sobolev Maps to the Circle
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Sobolev Maps to the Circle
Haim Brezis, Petru Mironescu (Gebundene Ausgabe, Englisch)
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Beschreibung
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 newdirections 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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
02.12.2021
Sprache
Englisch
EAN
9781071615102
Herausgeber
Springer US
Serien- oder Bandtitel
Progress in Nonlinear Differential Equations and Their Applications
Sonderedition
Nein
Autor
Haim Brezis, Petru Mironescu
Seitenanzahl
530
Auflage
1
Einbandart
Gebundene Ausgabe
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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