The Hodge-Laplacian
Mitrea, Dorina, Mitrea, Irina, Mitrea, Marius, Taylor, Michael
Produktnummer:
189a781670aae74aee98a96cc9f63b79d1
Autor: | Mitrea, Dorina Mitrea, Irina Mitrea, Marius Taylor, Michael |
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Themengebiete: | Laplace-Operator Randwertproblem Riemannscher Raum |
Veröffentlichungsdatum: | 10.10.2016 |
EAN: | 9783110482669 |
Auflage: | 1 |
Sprache: | Englisch |
Seitenzahl: | 518 |
Produktart: | Gebunden |
Verlag: | De Gruyter |
Untertitel: | Boundary Value Problems on Riemannian Manifolds |
Produktinformationen "The Hodge-Laplacian"
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

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