eBook - PDF
The Hodge–Laplacian
Boundary Value Problems on Riemannian Manifolds
- 624 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
The Hodge–Laplacian
Boundary Value Problems on Riemannian Manifolds
About this 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.
The 1-st edition of the "Hodge-Laplacian", De Gruyter Studies in Mathematics,
Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series "Geometric Harmonic Analysis" published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the "Hodge-Laplacian" and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition.
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.
The 1-st edition of the "Hodge-Laplacian", De Gruyter Studies in Mathematics,
Volume 64, 2016, is a trailblazer of its kind, having been written at a time when new results in Geometric Measure Theory have just emerged, or were still being developed. In particular, this monograph is heavily reliant on the bibliographical items. The latter was at the time an unpublished manuscript which eventually developed into the five-volume series "Geometric Harmonic Analysis" published by Springer 2022-2023. The progress registered on this occasion greatly impacts the contents of the "Hodge-Laplacian" and warrants revisiting this monograph in order to significantly sharpen and expand on previous results. This also allows us to provide specific bibliographical references to external work invoked in the new edition.
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.
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Yes, you can access The Hodge–Laplacian by Dorina Mitrea,Irina Mitrea,Marius Mitrea,Michael Taylor in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Preface to the first edition
- Preface to the second edition
- Contents
- Acknowledgement
- 1 Introduction and statement of main results
- 2 Geometric concepts and tools
- 3 Harmonic layer potentials associated with the Hodge–de Rham formalism on UR domains
- 4 Harmonic layer potentials associated with the Levi–Civita connection on UR domains
- 5 Dirichlet and Neumann problems for the Hodge–Laplacian in infinitesimally flat AR domains
- 6 Fatou theorems and integral representations for the Hodge–Laplacian in infinitesimally flat AR domains
- 7 Solvability of boundary problems for the Hodge–Laplacian in the Hodge–de Rham formalism
- 8 Additional results and applications
- 9 Tools from differential geometry, harmonic analysis, geometric measure theory, functional analysis, partial differential equations and Clifford analysis
- Bibliography
- Author index
- Subject index
- Symbol index