# Linear Partial Differential Operators

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

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

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

- 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 Springer Book Archive
- Print ISBN 978-3-642-46177-4
- Online ISBN 978-3-642-46175-0
- Series Print ISSN 0072-7830
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