# Linear Partial Differential Operators

• Lars Hörmander
Book

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

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

1. Lars Hörmander
Pages 63-96
2. Lars Hörmander
Pages 96-114
3. Lars Hörmander
Pages 114-155
4. ### Differential operators with variable coefficients

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

### Introduction

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.

### Keywords

Finite Operators distribution equation function functional analysis partial differential equation

#### Authors and affiliations

• Lars Hörmander
• 1
1. 1.University of Stockholm and at Stanford UniversitySweden

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-46175-0
• Copyright Information Springer-Verlag Berlin Heidelberg 1963
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-642-46177-4
• Online ISBN 978-3-642-46175-0
• Series Print ISSN 0072-7830