Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the completeness of the Papkovich potentials

Author: Robert F. Millar
Journal: Quart. Appl. Math. 41 (1984), 385-393
MSC: Primary 73C05; Secondary 31B99
DOI: https://doi.org/10.1090/qam/724050
MathSciNet review: 724050
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Abstract: The Papkovich representation for the elastostatic displacement vector in a domain $ D$ is considered. The possibility of eliminating from this representation either the scalar potential $ \chi $ or a rectangular component $ \psi $ of the vector potential $ \psi $ is examined. Earlier work is discussed and the connection is made with the oblique derivative problem of potential theory. A convexity requirement on the boundary of $ D$ is shown to be necessary in general in order that $ \chi $ or $ \psi $ may be eliminated.. A result of Stippes for a domain with an internal cavity is generalized, and two new classes of domains are found for which $ \chi $ may be eliminated.

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DOI: https://doi.org/10.1090/qam/724050
Article copyright: © Copyright 1984 American Mathematical Society

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