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The Hodge-Laplacian - Boundary Value Problems on Riemannian Manifolds (Hardcover)
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The Hodge-Laplacian - Boundary Value Problems on Riemannian Manifolds (Hardcover)
Series: De Gruyter Studies in Mathematics
Expected to ship within 12 - 17 working days
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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
General
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