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Geometric Measure Theory and Free Boundary Problems

Cetraro, Italy 2019

  • Book
  • © 2021

Overview

Authors:
  1. Guido De Philippis

    1. Courant Institute of Mathematical Sciences, New York, USA

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  2. Xavier Ros-Oton

    1. Department of Mathematics, University of Barcelona, Barcelona, Spain

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  3. Georg S. Weiss

    1. Faculty of Mathematics, University of Duisburg-Essen, Duisburg, Germany

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Editors:
  1. Matteo Focardi

    1. Department of Mathematics and Computer Science, University of Florence, Florence, Italy

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  2. Emanuele Spadaro

    1. Department of Mathematics, Sapienza University of Rome, Rome, Italy

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  • Presents three lectures by leading experts
  • Provides an in-depth exploration of recent advances
  • Includes extensive background and references

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2284)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction

    • Matteo Focardi, Emanuele Spadaro
    Pages 1-3

  3. A-Free Measures and Applications

    • Guido De Philippis
    Pages 5-35

  4. Regularity of Free Boundaries in Obstacle Problems

    • Xavier Ros-Oton
    Pages 37-88

  5. Bernoulli Type Free Boundary Problems and Water Waves

    • Georg S. Weiss
    Pages 89-136

  6. Back Matter

    Pages 137-138
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Keywords

About this book

This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro.

Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.


Authors, Editors and Affiliations

  • Department of Mathematics and Computer Science, University of Florence, Florence, Italy

    Matteo Focardi

  • Department of Mathematics, Sapienza University of Rome, Rome, Italy

    Emanuele Spadaro

  • Courant Institute of Mathematical Sciences, New York, USA

    Guido De Philippis

  • Department of Mathematics, University of Barcelona, Barcelona, Spain

    Xavier Ros-Oton

  • Faculty of Mathematics, University of Duisburg-Essen, Duisburg, Germany

    Georg S. Weiss

Bibliographic Information

  • Book Title: Geometric Measure Theory and Free Boundary Problems

  • Book Subtitle: Cetraro, Italy 2019

  • Authors: Guido De Philippis, Xavier Ros-Oton, Georg S. Weiss

  • Editors: Matteo Focardi, Emanuele Spadaro

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-65799-4

  • 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 2021

  • Softcover ISBN: 978-3-030-65798-7Published: 24 March 2021

  • eBook ISBN: 978-3-030-65799-4Published: 23 March 2021

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: V, 138

  • Number of Illustrations: 33 b/w illustrations

  • Topics: Analysis, Optimization

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