© 1972

Non-Homogeneous Boundary Value Problems and Applications

Volume II


Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 182)

Table of contents

  1. Front Matter
    Pages I-XI
  2. J. L. Lions, E. Magenes
    Pages 1-90
  3. J. L. Lions, E. Magenes
    Pages 157-207
  4. Back Matter
    Pages 208-244

About this book


I. In this second volume, we continue at first the study of non­ homogeneous boundary value problems for particular classes of evolu­ tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well­ defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap­ pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.


Boundary Boundary Value Problems Boundary value problem Randwertproblem Volume addition boundary element method character control equation evolution interpolation numerical analysis optimal control tool

Authors and affiliations

  1. 1.University of ParisFrance
  2. 2.University of PaviaItaly

Bibliographic information

  • Book Title Non-Homogeneous Boundary Value Problems and Applications
  • Book Subtitle Volume II
  • Authors Jacques Louis Lions
    Enrico Magenes
  • Series Title Die Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-05444-3
  • Softcover ISBN 978-3-642-65219-6
  • eBook ISBN 978-3-642-65217-2
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XII, 244
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Title of the original French edition: Problemes aus limites non homogenes et applications
  • Topics Numerical Analysis
  • Buy this book on publisher's site
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