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Geometric Harmonic Analysis V

Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems

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  • © 2023

Overview

Authors:
  1. Dorina Mitrea

    1. Department of Mathematics, Baylor University, Waco, USA

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  2. Irina Mitrea

    1. Dept Mathematics, Temple University, Philadelphia, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Marius Mitrea

    1. Department of Mathematics, Baylor University, Waco, USA

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  • State of the art, original, expansive account of elliptic boundary value problems
  • Elaborate treatment of Fredholm theory for boundary layer potential operators
  • The main results, in print here for the first time, bridge between geometry and partial differential equations

Part of the book series: Developments in Mathematics (DEVM, volume 76)

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About this book

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.

The ultimate goal in Volume V is to prove well-posedness and Fredholm solvability results concerning boundary value problems for elliptic second-order homogeneous constant (complex) coefficient systems, and domains of a rather general geometric nature. The formulation of the boundary value problems treated here is optimal from a multitude of points of view, having to do with geometry, functional analysis (through the consideration of a large variety of scales of function spaces), topology, and partial differential equations.


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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Distinguished Coefficient Tensors

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 1-70

  3. Failure of Fredholm Solvability for Weakly Elliptic Systems

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 71-112

  4. Quantifying Global and Infinitesimal Flatness

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 113-173

  5. Norm Estimates and Invertibility Results for SIO’s on Unbounded Boundaries

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 175-270

  6. Estimating Chord-Dot-Normal SIO’s on Domains with Compact Boundaries

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 271-364

  7. The Radon-Carleman Problem

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 365-396

  8. Fredholmness and Invertibility of Layer Potentials on Compact Boundaries

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 397-556

  9. Boundary Value Problems for Elliptic Systems in Rough Domains

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 557-924

  10. Back Matter

    Pages 925-994
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Authors and Affiliations

  • Department of Mathematics, Baylor University, Waco, USA

    Dorina Mitrea, Marius Mitrea

  • Dept Mathematics, Temple University, Philadelphia, USA

    Irina Mitrea

Bibliographic Information

  • Book Title: Geometric Harmonic Analysis V

  • Book Subtitle: Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems

  • Authors: Dorina Mitrea, Irina Mitrea, Marius Mitrea

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-31561-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-31560-2Published: 23 August 2023

  • Softcover ISBN: 978-3-031-31563-3Due: 23 September 2023

  • eBook ISBN: 978-3-031-31561-9Published: 22 August 2023

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XVI, 994

  • Number of Illustrations: 3 b/w illustrations, 3 illustrations in colour

  • Topics: Integral Transforms, Operational Calculus

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