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The Hodge-Laplacian

The Hodge-Laplacian


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About the Book

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


About the Author:

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


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Product Details
  • ISBN-13: 9783110482669
  • Publisher: De Gruyter
  • Publisher Imprint: de Gruyter
  • Height: 244 mm
  • No of Pages: 528
  • Series Title: de Gruyter Studies in Mathematics
  • Sub Title: Boundary Value Problems on Riemannian Manifolds
  • Width: 173 mm
  • ISBN-10: 3110482665
  • Publisher Date: 10 Oct 2016
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Spine Width: 33 mm
  • Weight: 1047 gr


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