The Hodge-Laplacian : boundary value problems on Riemannian manifolds / / Dorina Mitrea [and three others]

• Autore: Mitrea Dorina
• 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
• Classificazione: SK 540
• 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.: 9910798732003321
• Lo trovi qui: Univ. Federico II
• Serie: De Gruyter studies in mathematics ; ; Volume 64.