© 2002

Regularity Results for Nonlinear Elliptic Systems and Applications


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

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alain Bensoussan, Jens Frehse
    Pages 1-61
  3. Alain Bensoussan, Jens Frehse
    Pages 63-111
  4. Alain Bensoussan, Jens Frehse
    Pages 113-152
  5. Alain Bensoussan, Jens Frehse
    Pages 153-195
  6. Alain Bensoussan, Jens Frehse
    Pages 197-228
  7. Alain Bensoussan, Jens Frehse
    Pages 229-264
  8. Alain Bensoussan, Jens Frehse
    Pages 265-297
  9. Alain Bensoussan, Jens Frehse
    Pages 299-374
  10. Alain Bensoussan, Jens Frehse
    Pages 375-420
  11. Alain Bensoussan, Jens Frehse
    Pages 421-433
  12. Back Matter
    Pages 435-443

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.


Control Theory Nonlinear Systems Partial Differential Equations Regularity Analysis Variational Methods fluid mechanics game theory linear optimization mechanics model partial differential equation plasticity

Authors and affiliations

  1. 1.CNESParisFrance
  2. 2.Institut für Angewandte MathematikUniversität BonnBonnGermany

Bibliographic information

  • Book Title Regularity Results for Nonlinear Elliptic Systems and Applications
  • Authors Alain Bensoussan
    Jens Frehse
  • Series Title Applied Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-67756-7
  • Softcover ISBN 978-3-642-08726-4
  • eBook ISBN 978-3-662-12905-0
  • Series ISSN 0066-5452
  • Edition Number 1
  • Number of Pages XII, 443
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Partial Differential Equations
  • Buy this book on publisher's site
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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)