On the completeness of the Papkovich potentials
ROBERT F. MILLAR · Quarterly of Applied Mathematics · 1984
The Papkovich representation for the elastostatic displacement vector in a domain D D is considered. The possibility of eliminating from this representation either the scalar potential χ \chi or a rectangular component ψ \psi of the vector potential ψ \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 D is shown to be necessary in general in order that χ \chi or ψ \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 χ \chi may be eliminated.