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Non-Homogeneous Boundary Value Problems and Applications

Volume II

  • Book
  • © 1972


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

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Table of contents (3 chapters)


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.

Authors and Affiliations

  • University of Paris, France

    J. L. Lions

  • University of Pavia, Italy

    E. Magenes

Bibliographic Information

  • Book Title: Non-Homogeneous Boundary Value Problems and Applications

  • Book Subtitle: Volume II

  • Authors: J. L. Lions, E. Magenes

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI:

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag, Berlin · Heidelberg 1972

  • Softcover ISBN: 978-3-642-65219-6Published: 12 November 2011

  • eBook ISBN: 978-3-642-65217-2Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XII, 244

  • Additional Information: Title of the original French edition: Problemes aus limites non homogenes et applications

  • Topics: Numerical Analysis

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