Non-Homogeneous Boundary Value Problems and Applications

Volume II

  • J. L. Lions
  • E. Magenes

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

Introduction

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.

Keywords

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

  • J. L. Lions
    • 1
  • E. Magenes
    • 2
  1. 1.University of ParisFrance
  2. 2.University of PaviaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65217-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1972
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65219-6
  • Online ISBN 978-3-642-65217-2
  • Series Print ISSN 0072-7830
  • About this book
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