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Geometry of PDEs and Related Problems

Cetraro, Italy 2017

  • Book
  • © 2018

Overview

Authors:
  1. Xavier Cabré

    1. Departament de Matemàtiques, ICREA and Universitat Politècnica de Catalunya, Barcelona, Spain

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  2. Antoine Henrot

    1. Institut Elie Cartan – Faculté des Sciences et Technologies, Université de Lorraine, Vandoeuvre-les-Nancy, France

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  3. Daniel Peralta-Salas

    1. Consejo Superior de Investigaciones Científicas, Instituto de Ciencias Matemáticas, Madrid, Spain

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  4. Wolfgang Reichel

    1. Institute for Analysis, Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

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  5. Henrik Shahgholian

    1. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

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Editors:
  1. Chiara Bianchini

    1. Dipt di Matematica e Informatica Ulisse Dini, Università degli Studi di Firenze, Firenze, Italy

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  2. Antoine Henrot

    1. Institut Elie Cartan – Faculté des Sciences et Technologies, Université de Lorraine, Vandoeuvre-les-Nancy, France

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  3. Rolando Magnanini

    1. Dipt di Matematica e Informatica Ulisse Dini, Università degli Studi di Firenze, Firenze, Italy

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  • Provides an excellent, up-to-date and friendly introduction to the hot topics in the study of PDEs
  • Will attract potential readers from several areas of mathematics
  • Presents numerous open problems that are discussed in some detail

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2220)

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Stable Solutions to Some Elliptic Problems: Minimal Cones, the Allen-Cahn Equation, and Blow-Up Solutions

    • Xavier Cabré, Giorgio Poggesi
    Pages 1-45

  3. Isoperimetric Inequalities for Eigenvalues of the Laplacian

    • Antoine Henrot
    Pages 47-88

  4. Topological Aspects of Critical Points and Level Sets in Elliptic PDEs

    • Alberto Enciso, Daniel Peralta-Salas
    Pages 89-119

  5. Symmetry Properties for Solutions of Higher-Order Elliptic Boundary Value Problems

    • Wolfgang Reichel
    Pages 121-145

  6. Recent Trends in Free Boundary Regularity

    • Henrik Shahgholian
    Pages 147-196

  7. Back Matter

    Pages 197-198
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Keywords

About this book

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references.

Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Authors, Editors and Affiliations

  • Dipt di Matematica e Informatica Ulisse Dini, Università degli Studi di Firenze, Firenze, Italy

    Chiara Bianchini, Rolando Magnanini

  • Institut Elie Cartan – Faculté des Sciences et Technologies, Université de Lorraine, Vandoeuvre-les-Nancy, France

    Antoine Henrot, Antoine Henrot

  • Departament de Matemàtiques, ICREA and Universitat Politècnica de Catalunya, Barcelona, Spain

    Xavier Cabré

  • Consejo Superior de Investigaciones Científicas, Instituto de Ciencias Matemáticas, Madrid, Spain

    Daniel Peralta-Salas

  • Institute for Analysis, Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Wolfgang Reichel

  • Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Henrik Shahgholian

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