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Birkhäuser

Variational Problems with Concentration

  • Book
  • © 1999

Overview

Authors:
  1. Martin Flucher

    1. SHERPA’X AG, Solothurn, Switzerland

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 36)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Introduction

    • Martin Flucher
    Pages 1-11

  3. P-Capacity

    • Martin Flucher
    Pages 13-15

  4. Generalized Sobolev Inequality

    • Martin Flucher
    Pages 17-22

  5. Concentration Compactness Alternatives

    • Martin Flucher
    Pages 23-33

  6. Compactness Criteria

    • Martin Flucher
    Pages 35-42

  7. Entire Extremals

    • Martin Flucher
    Pages 43-50

  8. Concentration and Limit Shape of Low Energy Extremals

    • Martin Flucher
    Pages 51-62

  9. Robin Functions

    • Martin Flucher
    Pages 63-79

  10. P-Capacity of Small Sets

    • Martin Flucher
    Pages 81-86

  11. P-Harmonic Transplantation

    • Martin Flucher
    Pages 87-90

  12. Identification of Concentration Points, Subconformal Case

    • Martin Flucher
    Pages 91-95

  13. Conformal Low Energy Limits

    • Martin Flucher
    Pages 97-107

  14. Applications

    • Martin Flucher
    Pages 109-115

  15. Bernoulli’s Free-boundary Problem

    • Martin Flucher
    Pages 117-129

  16. Vortex Motion in Two Dimensional Hydrodynamics

    • Martin Flucher
    Pages 131-149

  17. Back Matter

    Pages 151-163
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Keywords

About this book

To start with we describe two applications of the theory to be developed in this monograph: Bernoulli's free-boundary problem and the plasma problem. Bernoulli's free-boundary problem This problem arises in electrostatics, fluid dynamics, optimal insulation, and electro chemistry. In electrostatic terms the task is to design an annular con­ denser consisting of a prescribed conducting surface 80. and an unknown conduc­ tor A such that the electric field 'Vu is constant in magnitude on the surface 8A of the second conductor (Figure 1.1). This leads to the following free-boundary problem for the electric potential u. -~u 0 in 0. \A, u 0 on 80., u 1 on 8A, 8u Q on 8A. 811 The unknowns are the free boundary 8A and the potential u. In optimal in­ sulation problems the domain 0. \ A represents the insulation layer. Given the exterior boundary 80. the problem is to design an insulating layer 0. \ A of given volume which minimizes the heat or current leakage from A to the environment ]R.n \ n. The heat leakage per unit time is the capacity of the set A with respect to n. Thus we seek to minimize the capacity among all sets A c 0. of equal volume.

Reviews

"This material is very rich, because various alternatives are possible. The book provides a good systematic overview of this difficult topic."

--Zentralblatt Math

Authors and Affiliations

  • SHERPA’X AG, Solothurn, Switzerland

    Martin Flucher

Bibliographic Information

  • Book Title: Variational Problems with Concentration

  • Authors: Martin Flucher

  • Series Title: Progress in Nonlinear Differential Equations and Their Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8687-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1999

  • Hardcover ISBN: 978-3-7643-6136-5Published: 01 July 1999

  • Softcover ISBN: 978-3-0348-9729-7Published: 02 November 2012

  • eBook ISBN: 978-3-0348-8687-1Published: 06 December 2012

  • Series ISSN: 1421-1750

  • Series E-ISSN: 2374-0280

  • Edition Number: 1

  • Number of Pages: VIII, 163

  • Topics: Analysis

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