Linear Partial Differential Operators

1. Front Matter

   Pages I-VII

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2. Functional analysis

   1. Distribution theory

      • Lars Hörmander

      Pages 1-33

   2. Some special spaces of distributions

      • Lars Hörmander

      Pages 33-62

3. Differential operators with constant coefficients

   1. Existence and approximation of solutions of differential equations

      • Lars Hörmander

      Pages 63-96

   2. Interior regularity of solutions of differential equations

      • Lars Hörmander

      Pages 96-114

   3. The Cauchy problem (constant coefficients)

      • Lars Hörmander

      Pages 114-155

4. Differential operators with variable coefficients

   1. Differential equations which have no solutions

      • Lars Hörmander

      Pages 156-170

   2. Differential operators of constant strength

      • Lars Hörmander

      Pages 170-180

   3. Differential operators with simple characteristics

      • Lars Hörmander

      Pages 180-230

   4. The Cauchy problem (variable coefficients)

      • Lars Hörmander

      Pages 230-241

   5. Elliptic boundary problems

      • Lars Hörmander

      Pages 242-274

5. Back Matter

   Pages 275-287

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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
• partial differential equations

• University of Stockholm and at Stanford University, Sweden

  Lars Hörmander

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