The Hodge-Laplacian : : Boundary Value Problems on Riemannian Manifolds / / Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor.

• Superior document: Title is part of eBook package: De Gruyter DG Plus DeG Package 2016 Part 1
• VerfasserIn: Mitrea, Dorina,; Mitrea, Irina,; Mitrea, Marius,; Taylor, Michael,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2016]; ©2016
• Year of Publication: 2016
• Language: English
• Series: De Gruyter Studies in Mathematics , 64
• Physical Description: 1 online resource (X, 518 p.)
• Other title: 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
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110484380; 9783110762501; 9783110701005; 9783110494938; 9783110485103; 9783110485288
• ISSN: 0179-0986
• DOI: 10.1515/9783110484380
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor.

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