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The Hodge-Laplacian
Boundary Value Problems on Riemannian Manifolds
Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor
€ 370,95
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Omschrijving
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:
Preface
Introduction and Statement of Main Results
Geometric Concepts and Tools
Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains
Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains
Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains
Fatou Theorems and Integral Representations for the Hodge-Laplacian on Regular SKT Domains
Solvability of Boundary Problems for the Hodge-Laplacian in the Hodge-de Rham Formalism
Additional Results and Applications
Further Tools from Differential Geometry, Harmonic Analysis, Geometric Measure Theory, Functional Analysis, Partial Differential Equations, and Clifford Analysis
Bibliography
Index
Specificaties
Betrokkenen
- Auteur(s):
- Uitgeverij:
Inhoud
- Aantal bladzijden:
- 528
- Taal:
- Engels
- Reeks:
- Reeksnummer:
- nr. 64
Eigenschappen
- Productcode (EAN):
- 9783110482669
- Verschijningsdatum:
- 10/10/2016
- Uitvoering:
- Hardcover
- Formaat:
- Genaaid
- Afmetingen:
- 170 mm x 240 mm
- Gewicht:
- 1018 g
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