Overview
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 The latter was at the time an unpublished manuscript which eventually developed into the five-volume series “Geometric Harmonic Analysis” published by Springer 2022-2023.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.
Full Product Details
Author: Dorina Mitrea ,
Irina Mitrea ,
Marius Mitrea ,
Michael Taylor
Publisher: De Gruyter
Imprint: De Gruyter
Edition: 2nd revised edition
Weight: 1.162kg
ISBN: 9783111480985
ISBN 10: 3111480984
Pages: 624
Publication Date: 27 January 2025
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: Available To Order
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Reviews
""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
Author Information
D. Mitrea and M. Mitrea, Baylor Univ., USA; I. Mitrea, Temple Univ., USA; M. Taylor, Univ. of North Carolina, USA.
