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Regularity Results for Nonlinear Elliptic Systems and Applications

  • Book
  • © 2002

Overview

Authors:
  1. Alain Bensoussan

    1. CNES, Paris, France

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  2. Jens Frehse

    1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Applied Mathematical Sciences (AMS, volume 151)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xii
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  2. General Technical Results

    • Alain Bensoussan, Jens Frehse
    Pages 1-61

  3. General Regularity Results

    • Alain Bensoussan, Jens Frehse
    Pages 63-111

  4. Nonlinear Elliptic Systems Arising from Stochastic Games

    • Alain Bensoussan, Jens Frehse
    Pages 113-152

  5. Nonlinear Elliptic Systems Arising from Ergodic Control

    • Alain Bensoussan, Jens Frehse
    Pages 153-195

  6. Harmonic Mappings

    • Alain Bensoussan, Jens Frehse
    Pages 197-228

  7. Nonlinear Elliptic Systems Arising from the Theory of Semiconductors

    • Alain Bensoussan, Jens Frehse
    Pages 229-264

  8. Stationary Navier—Stokes Equations

    • Alain Bensoussan, Jens Frehse
    Pages 265-297

  9. Strongly Coupled Elliptic Systems

    • Alain Bensoussan, Jens Frehse
    Pages 299-374

  10. Dual Approach to Nonlinear Elliptic Systems

    • Alain Bensoussan, Jens Frehse
    Pages 375-420

  11. Nonlinear Elliptic Systems Arising from plasticity Theory

    • Alain Bensoussan, Jens Frehse
    Pages 421-433

  12. Back Matter

    Pages 435-443
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Keywords

About this book

The book collects many techniques that are helpul in obtaining regularity results for solutions of nonlinear systems of partial differential equations. They are then applied in various cases to provide useful examples and relevant results, particularly in fields like fluid mechanics, solid mechanics, semiconductor theory, or game theory.
In general, these techniques are scattered in the journal literature and developed in the strict context of a given model. In the book, they are presented independently of specific models, so that the main ideas are explained, while remaining applicable to various situations. Such a presentation will facilitate application and implementation by researchers, as well as teaching to students.

Reviews

From the reviews:

"The book under review presents several topics of the regularity theory for nonlinear elliptic equations and systems which have been developed in recent years. … It may serve for teaching to higher graduate students and for researchers in the field of nonlinear PDE’s." (Joachim Naumann, Zentralblatt MATH, Vol. 1055, 2005)

"It is a pleasure to review this new book by Bensoussan and Frehse; indeed this work covers remarkable, finely selected, updated material … . this book is a very interesting and useful source of material for those interested in the latest developments of regularity theory of solutions of nonlinear elliptic systems. … the book is an essential companion to the standard monographs already available and it is bound to become a standard and inevitable item in any list of references on the subject." (Giuseppe Mingione, Mathematical Reviews, 2004 a)

Authors and Affiliations

  • CNES, Paris, France

    Alain Bensoussan

  • Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Jens Frehse

Bibliographic Information

  • Book Title: Regularity Results for Nonlinear Elliptic Systems and Applications

  • Authors: Alain Bensoussan, Jens Frehse

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-12905-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-540-67756-7Published: 12 June 2002

  • Softcover ISBN: 978-3-642-08726-4Published: 18 December 2010

  • eBook ISBN: 978-3-662-12905-0Published: 17 April 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XII, 443

  • Topics: Partial Differential Equations

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