The Hodge-Laplacian
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Home > Mathematics and Science Textbooks > Mathematics > Geometry > Differential and Riemannian geometry > The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds(64 De Gruyter Studies in Mathematics)
The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds(64 De Gruyter Studies in Mathematics)

The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds(64 De Gruyter Studies in Mathematics)


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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.

Review :
"The book represents the cumulation of a large body of work of the authors. Nonetheless, it is essentially self-contained, including the main geometric and analytic preliminaries. There are a large number of variations of settings. But the book is very well structured, avoiding potential confusions here." Mathematical Reviews


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Product Details
  • ISBN-13: 9783110483390
  • Publisher: De Gruyter
  • Publisher Imprint: de Gruyter
  • Language: English
  • Series Title: 64 De Gruyter Studies in Mathematics
  • ISBN-10: 3110483394
  • Publisher Date: 10 Oct 2016
  • Binding: Digital (delivered electronically)
  • No of Pages: 528
  • Sub Title: Boundary Value Problems on Riemannian Manifolds


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