Existence and approximation of solutions of differential equations

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


In the theory of differential operators with constant coefficients developed in this chapter and the next, the existence of a fundamental solution proved in section 3.1 has a central place. This result was first obtained in full generality by Ehrenpreis [1] and by Malgrange [1]. Our proof follows that of Malgrange [1] with the modifications introduced by Hörmander [2] in order to obtain the best possible local regularity properties. This improvement is necessary for the passage to operators with variable coefficients in Chapter VII and for the study of interior regularity properties in Chapter IV.


Differential Operator Convex Hull Compact Subset Fundamental Solution Half Space 
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Copyright information

© Springer-Verlag OHG, Berlin · Göttingen · Heidelberg 1963

Authors and Affiliations

  1. 1.University of Stockholm and at Stanford UniversitySweden

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