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Non-Homogeneous Boundary Value Problems and Applications

Vol. 1

  • Book
  • © 1972

Overview

Authors:
  1. J. L. Lions

    1. University of Paris, France

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  2. E. Magenes

    1. University of Pavia, Italy

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 181)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Hilbert Theory of Trace and Interpolation Spaces

    • J. L. Lions, E. Magenes
    Pages 1-108

  3. Elliptic Operators, Hilbert Theory

    • J. L. Lions, E. Magenes
    Pages 109-226

  4. Variational Evolution Equations

    • J. L. Lions, E. Magenes
    Pages 227-308

  5. Back Matter

    Pages 309-360
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Keywords

About this book

1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con­ j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.

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: Vol. 1

  • Authors: J. L. Lions, E. Magenes

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-642-65161-8

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag, Berlin Heidelberg 1972

  • Softcover ISBN: 978-3-642-65163-2Published: 15 November 2011

  • eBook ISBN: 978-3-642-65161-8Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XVI, 360

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

  • Topics: Analysis

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