Zum Hauptinhalt springen Zur Suche springen Zur Hauptnavigation springen
Herzlich Willkommen!
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 The latter was at the time an unpublished manuscript which eventually developed into the five-volume series “Geometric Harmonic Analysis” published by Springer 2022-2023.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.
Autor: Mitrea, Dorina Mitrea, Irina Mitrea, Marius Taylor, Michael
ISBN: 9783111480985
Auflage: 2
Sprache: Englisch
Seitenzahl: 610
Produktart: Gebunden
Verlag: De Gruyter
Veröffentlicht: 27.01.2025
Untertitel: Boundary Value Problems on Riemannian Manifolds
Schlagworte: Boundary value problem Laplace-Operator Laplacian Randwertproblem Riemannian space Riemannscher Raum
D. Mitrea and M. Mitrea, Baylor Univ., USA; I. Mitrea, Temple Univ., USA; M. Taylor, Univ. of North Carolina, USA.