On the completeness of the Papkovich potentials

Millar, Robert F.

doi:10.1090/qam/724050

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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