The Hodge-Laplacian : boundary value problems on Riemannian manifolds
著者
書誌事項
The Hodge-Laplacian : boundary value problems on Riemannian manifolds
(De Gruyter studies in mathematics, v. 64)
De Gruyter, c2016
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注記
Other authors: Irina Mitrea, Marius Mitrea, Michael Taylor
Includes bibliographical references (p. [501]-506) and indexes
内容説明・目次
内容説明
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 Calderon-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, Poincare, 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
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