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| Verfasst von: | Mitrea, Dorina [VerfasserIn]  |
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| | Mitrea, Irina [VerfasserIn] |
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| | Mitrea, Marius [VerfasserIn] |
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| | Taylor, Michael Eugene [VerfasserIn] |
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| Titel: | The Hodge-Laplacian |
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| Titelzusatz: | boundary value problems on Riemannian manifolds |
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| Institutionen: | Walter de Gruyter GmbH & Co. KG [Verlag] |
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| Verf.angabe: | Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor |
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| Ausgabe: | 2nd edition |
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| Verlagsort: | Berlin ; Boston |
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| Verlag: | De Gruyter |
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| E-Jahr: | 2025 |
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| Jahr: | [2025] |
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| Umfang: | 1 Online-Ressource (XI, 608 Seiten) |
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| Gesamttitel/Reihe: | De Gruyter studies in mathematics ; volume 64 |
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| | De Gruyter eBook-Paket Mathematik |
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| ISBN: | 978-3-11-148140-1 |
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| | 978-3-11-148389-4 |
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| Abstract: | The core of this monograph is the development of tools to derive well-posedness results in very general geometric settings for elliptic differential operators. A new generation of Calderón-Zygmund theory is developed for variable coefficient singular integral operators, which turns out to be particularly versatile in dealing with boundary value problems for the Hodge-Laplacian on uniformly rectifiable subdomains of Riemannian manifolds via boundary layer methods. In addition to absolute and relative boundary conditions for differential forms, this monograph treats the Hodge-Laplacian equipped with classical Dirichlet, Neumann, Transmission, Poincaré, and Robin boundary conditions in regular Semmes-Kenig-Toro domains.Lying at the intersection of partial differential equations, harmonic analysis, and differential geometry, this text is suitable for a wide range of PhD students, researchers, and professionals. Contents:PrefaceIntroduction and Statement of Main ResultsGeometric Concepts and ToolsHarmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR DomainsHarmonic Layer Potentials Associated with the Levi-Civita Connection on UR DomainsDirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT DomainsFatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT DomainsSolvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham FormalismAdditional Results and ApplicationsFurther Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford AnalysisBibliographyIndex |
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| DOI: | doi:10.1515/9783111481401 |
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| URL: | Volltext: https://dx.doi.org/10.1515/9783111481401 |
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| | Volltext: https://doi.org/10.1515/9783111481401 |
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| | Verlag: https://www.degruyterbrill.com/isbn/9783111481401 |
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| | Cover: https://www.degruyterbrill.com/document/cover/isbn/9783111481401/original |
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| | DOI: https://doi.org/10.1515/9783111481401 |
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| Datenträger: | Online-Ressource |
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| Sprache: | eng |
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| Bibliogr. Hinweis: | Erscheint auch als : Druck-Ausgabe: Mitrea, Dorina, 1965 - : The Hodge-Laplacian. - 2nd edition. - Berlin : De Gruyter, 2025. - XI, 608 Seiten |
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| Sach-SW: | MATHEMATICS / Differential Equations / Partial |
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| K10plus-PPN: | 1915198240 |
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| Verknüpfungen: | → Übergeordnete Aufnahme |
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| Lokale URL UB: |  Zum Volltext |
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