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The Hodge-Laplacian : boundary value problems on Riemannian manifolds /
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 partic...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
De Gruyter,
2016.
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| Colección: | De Gruyter studies in mathematics ;
Volume 64. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface ; Contents ; 1 Introduction and Statement of Main Results ; 1.1 First Main Result: Absolute and Relative Boundary Conditions ; 1.2 Other Problems Involving Tangential and Normal Components of Harmonic Forms ; 1.3 Boundary Value Problems for Hodge-Dirac Operators; 1.4 Dirichlet, Neumann, Transmission, Poincaré, and Robin-Type Boundary Problems 1.5 Structure of the Monograph ; 2 Geometric Concepts and Tools ; 2.1 Differential Geometric Preliminaries ; 2.2 Elements of Geometric Measure Theory; 2.3 Sharp Integration by Parts Formulas for Differential Forms in Ahlfors Regular Domains 2.4 Tangential and Normal Differential Forms on Ahlfors Regular Sets ; 3 Harmonic Layer Potentials Associated with the Hodge-de Rham Formalism on UR Domains; 3.1 A Fundamental Solution for the Hodge-Laplacian 3.2 Layer Potentials for the Hodge-Laplacian in the Hodge-de Rham Formalism ; 3.3 Fredholm Theory for Layer Potentials in the Hodge-de Rham Formalism ; 4 Harmonic Layer Potentials Associated with the Levi-Civita Connection on UR Domains; 4.1 The Definition and Mapping Properties of the Double Layer 4.2 The Double Layer on UR Subdomains of Smooth Manifolds ; 4.3 Compactness of the Double Layer on Regular SKT Domains ; 5 Dirichlet and Neumann Boundary Value Problems for the Hodge-Laplacian on Regular SKT Domains.