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 is considered. The possibility of eliminating from this representation either the scalar potential or a rectangular component of the vector potential 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 is shown to be necessary in general in order that or 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 may be eliminated.

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DOI:
https://doi.org/10.1090/qam/724050

Article copyright:
© Copyright 1984
American Mathematical Society