© 1963

Linear Partial Differential Operators


Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 116)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Functional analysis

    1. Lars Hörmander
      Pages 1-33
    2. Lars Hörmander
      Pages 33-62
  3. Differential operators with constant coefficients

  4. Differential operators with variable coefficients

    1. Lars Hörmander
      Pages 156-170
    2. Lars Hörmander
      Pages 170-180
    3. Lars Hörmander
      Pages 230-241
    4. Lars Hörmander
      Pages 242-274
  5. Back Matter
    Pages 275-287

About this book


The aim of this book is to give a systematic study of questions con­ cerning existence, uniqueness and regularity of solutions of linear partial differential equations and boundary problems. Let us note explicitly that this program does not contain such topics as eigenfunction expan­ sions, although we do give the main facts concerning differential operators which are required for their study. The restriction to linear equations also means that the trouble of achieving minimal assumptions concerning the smoothness of the coefficients of the differential equations studied would not be worth while; we usually assume that they are infinitely differenti­ able. Functional analysis and distribution theory form the framework for the theory developed here. However, only classical results of functional analysis are used. The terminology employed is that of BOURBAKI. To make the exposition self-contained we present in Chapter I the elements of distribution theory that are required. With the possible exception of section 1.8, this introductory chapter should be bypassed by a reader who is already familiar with distribution theory.


Finite Operators distribution equation function functional analysis partial differential equation

Authors and affiliations

  1. 1.University of Stockholm and at Stanford UniversitySweden

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