The Hodge-Laplacian : boundary value problems on Riemannian manifolds

Author(s)

• Mitrea, Dorina (Dorina Irena Rita)
• Mitrea, Irina
• Mitrea, Marius
• Taylor, Michael

Bibliographic Information

The Hodge-Laplacian : boundary value problems on Riemannian manifolds

Dorina Mitrea ... [et al.]

（De Gruyter studies in mathematics, v. 64）

De Gruyter, c2016

Note

Other authors: Irina Mitrea, Marius Mitrea, Michael Taylor

Includes bibliographical references (p. [501]-506) and indexes

Description and Table of Contents

Description

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

by "Nielsen BookData"

Details

• NCID: BB22302707
• ISBN:
  • 9783110482669
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin
• Pages/Volumes: ix, 516 p.
• Size: 25 cm
• Classification:
  • LCC : QA649
  • DC23 : 516.3/73
• Subject Headings:
  • LCSH : Riemannian manifolds
  • LCSH : Boundary value problems
• Parent Bibliography ID:
  • BA00079423