The Hodge-Laplacian - Boundary Value Problems on Riemannian Manifolds (Hardcover)

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

Imprint:	De Gruyter
Country of origin:	Germany
Series:	De Gruyter Studies in Mathematics
Release date:	October 2016
First published:	2016
Authors:	Dorina Mitrea • Irina Mitrea • Marius Mitrea • Michael Taylor
Dimensions:	240 x 170 x 33mm (L x W x T)
Format:	Hardcover - Cloth over boards
Pages:	528
ISBN-13:	978-3-11-048266-9
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
LSN:	3-11-048266-5
Barcode:	9783110482669

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