| The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds Contributor(s): Mitrea, Dorina (Author), Mitrea, Irina (Author), Mitrea, Marius (Author) |
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ISBN: 3110482665 ISBN-13: 9783110482669 Publisher: de Gruyter OUR PRICE: $218.50 Product Type: Hardcover - Other Formats Published: October 2016 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Mathematics | Differential Equations - Partial |
| Series: de Gruyter Studies in Mathematics |
| Physical Information: 1.3" H x 6.8" W x 9.6" (2.20 lbs) 528 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |
Contributor Bio(s): Mitrea, Dorina: - D. Mitrea and M. Mitrea, Univ. of Missouri, USA;I. Mitrea, Temple Univ., Philadelphia, USA;M. Taylor, Univ. of North Carolina, USA. |