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On the Agmon-Miranda maximum principle for solutions of strongly elliptic equations in domains of ℝnwith conical points

✍ Scribed by Vladimir G. Maz'ya; Jürgen Rossmann

Publisher: Springer
Year: 1992
Tongue: English
Weight: 954 KB
Volume: 10
Category: Article
ISSN: 0232-704X
DOI: 10.1007/bf00130916

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✦ Synopsis

In this paper the Agmon-Miranda maximum principle for solutions of strongly elliptic differential equations Lu = 0 in a bounded domain G with a conical point is considered. Necessary and sufficient conditions for the validity of this principle are given both for smooth solutions of the equation Lu = 0 in G and for the generalized solution of the problem Lu = 0 in G, Dku = g. on G (k = 0, ... , m-1). It will be shown that for every elliptic operator L of order 2m > 2 there exists such a cone in R" (n > 4) that the Agmon-Miranda maximum principle fails in this cone.

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