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Birkhäuser

Singular Integral Operators, Quantitative Flatness, and Boundary Problems

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  • © 2022

Overview

  • Presents many significant new results on the topic of singular integral operators and boundary value problems
  • Contributes to ongoing efforts to establish a bridge between analysis and geometry
  • Includes many complete proofs appearing in publication for the first time

Part of the book series: Progress in Mathematics (PM, volume 344)

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Table of contents (8 chapters)

Keywords

About this book

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.

Authors and Affiliations

  • Institute of Mathematical Sciences, Madrid, Spain

    Juan José Marín

  • Institute of Mathematical Sciences, Universidad Autónoma de Madrid, Madrid, Spain

    José María Martell

  • Department of Mathematics, Baylor University, Waco, USA

    Dorina Mitrea, Marius Mitrea

  • Department of Mathematics, Temple University, Philadelphia, USA

    Irina Mitrea

About the authors

Juan José Marín is a harmonic analyst whose research interests also include boundary value problems and geometric measure theory. He received a Ph.D. in mathematics in 2019 from Universidad Aut\'onoma de Madrid and Instituto de Ciencias Matem\'aticas, Spain, working under the supervision of José María Martell and Marius Mitrea.

José María Martell is a mathematician specializing in the areas of harmonic analysis, partial differential equations, and geometric measure theory. He received a Ph.D. in mathematics from Universidad Autónoma de Madrid, Spain, working under the supervision of José Garcia-Cuerva. José María Martell is currently serving as the director of Instituto de Matemáticas, Spain.

Dorina Mitrea is a mathematician specializing in the areas of harmonic analysis, partial differential equations, geometric measure theory, and global analysis. She received a Ph.D. in mathematics from the University of Minnesota, working under the supervision of Eugene Fabes. Dorina Mitrea is currently serving as the chair of the Department of Mathematics, Baylor University, USA.

Irina Mitrea is an L.H. Carnell Professor and chair of the Department of Mathematics at Temple University whose expertise lies at the interface between the areas of harmonic analysis, partial differential equations, and geometric measure theory. She received her Ph.D. in mathematics from the University of Minnesota, working under the supervision of Carlos Kenig and Mikhail Safanov. 

Irina Mitrea is a Fellow of the American Mathematical Society and a Fellow of the Association for Women in Mathematics. She received a Simons Foundation Fellowship, a Von Neumann Fellowship at the Institute for Advanced Study, Princeton, and is a recipient of the Ruth Michler Memorial Prize from the Association for Women in Mathematics.

Marius Mitrea is a mathematician whose research interests lay at the confluence between harmonic analysis, partial differential equations, geometric measure theory, global analysis, and scattering. He received a Ph.D. in mathematics from the University of South Carolina, USA, working under the supervision of Björn D. Jawerth. Marius Mitrea is a Fellow of the American Mathematical Society.







Bibliographic Information

  • Book Title: Singular Integral Operators, Quantitative Flatness, and Boundary Problems

  • Authors: Juan José Marín, José María Martell, Dorina Mitrea, Irina Mitrea, Marius Mitrea

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-08234-4

  • Publisher: Birkhäuser 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 2022

  • Hardcover ISBN: 978-3-031-08233-7Published: 30 September 2022

  • Softcover ISBN: 978-3-031-08236-8Published: 02 October 2023

  • eBook ISBN: 978-3-031-08234-4Published: 29 September 2022

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: VIII, 601

  • Number of Illustrations: 2 b/w illustrations, 3 illustrations in colour

  • Topics: Potential Theory, Integral Equations, Analysis, Measure and Integration

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