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The Hodge–Laplacian
Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor (Gebundene Ausgabe, Englisch)
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Beschreibung
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 The latter was at the time an unpublished manuscript which eventually developed into the five-volume series “Geometric Harmonic Analysis” published by Springer 2022-2023.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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
27.01.2025
Sprache
Englisch
EAN
9783111480985
Herausgeber
De Gruyter
Serien- oder Bandtitel
De Gruyter Studies in Mathematics
Sonderedition
Nein
Autor
Dorina Mitrea, Irina Mitrea, Marius Mitrea, Michael Taylor
Seitenanzahl
610
Auflage
2
Einbandart
Gebundene Ausgabe
Hersteller: De Gruyter GmbH, Genthiner Straße 13, Berlin, Deutschland, 10785, productsafety@degruyterbrill.com
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