The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds - Couverture rigide

Mitrea, Dorina; Mitrea, Irina; Mitrea, Marius; Taylor, Michael

Couverture rigide

ISBN 10 : 3110482665 ISBN 13 : 9783110482669

Editeur : De Gruyter, 2016

Synopsis

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

A propos du livre

À propos de l'auteur

D. Mitrea and M. Mitrea, Univ. of Missouri, USA;I. Mitrea, Temple Univ., Philadelphia, USA;M. Taylor, Univ. of North Carolina, USA.

Détails de l'édition

• Éditeur: De Gruyter
• Date d'édition: 2016
• Langue: anglais
• ISBN 10: 3110482665
• ISBN 13: 9783110482669
• Reliure: Relié
• Nombre de pages: 528
• Coordonnées du fabricant: non disponible
• Personne responsable: KreGa Onlinehandel GmbH; 4950000000000; info@krega-onlinehandel.de; ; Birkenweg 31; Brakel; 33034; Allemagne