The Hodge-Laplacian : boundary value problems on Riemannian manifolds / / Dorina Mitrea [and three others]
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| Autore: |
Mitrea Dorina
|
| Titolo: |
The Hodge-Laplacian : boundary value problems on Riemannian manifolds / / Dorina Mitrea [and three others]
|
| Pubblicazione: | Berlin, [Germany] ; ; Boston, [Massachusetts] : , : De Gruyter, , 2016 |
| ©2016 | |
| Descrizione fisica: | 1 online resource (528 pages) |
| Disciplina: | 516.3/73 |
| Soggetto topico: | Riemannian manifolds |
| Boundary value problems | |
| Soggetto genere / forma: | Electronic books. |
| Persona (resp. second.): | MitreaDorina <1965-> |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | Frontmatter -- Preface -- Contents -- 1. Introduction and Statement of Main Results -- 2. Geometric Concepts and Tools -- 3. Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains -- 4. Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains -- 5. Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains -- 6. Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains -- 7. Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism -- 8. Additional Results and Applications -- 9. Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis -- Bibliography -- Index -- Backmatter |
| Sommario/riassunto: | 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 |
| Titolo autorizzato: | The Hodge-Laplacian |
| ISBN: | 3-11-048339-4 |
| 3-11-048438-2 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910465984603321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
De Gruyter studies in mathematics ; ; Volume 64.