The Hodge–Laplacian: Boundary Value Problems on Riemannian Manifolds - De Gruyter Studies in Mathematics - Dorina Mitrea - Livros - De Gruyter - 9783111480985 - 27 de janeiro de 2025
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Dorina Mitrea
The Hodge–Laplacian: Boundary Value Problems on Riemannian Manifolds - De Gruyter Studies in Mathematics 2nd revised edition

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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 The latter was at the time an unpublished manuscript which eventually developed into the five-volume series “Geometric Harmonic Analysis” published by Springer 2022-2023.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.

Mídia Livros     Hardcover Book   (Livro com lombada e capa dura)
Lançado 27 de janeiro de 2025
ISBN13 9783111480985
Editoras De Gruyter
Páginas 624
Dimensões 150 × 220 × 20 mm   ·   1,16 kg

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