SOME BOUNDARY VALUE PROBLEMS IN POTENTIAL THEORY

Abstract

It is shown that a class of axially symmetric boundary value problems in potential theory for the region external to a lens may be reduced to problems in two-dimensional potential theory. The solution for the general axially symmetric Dirichlet problem is obtained and it is shown that the Stokes stream function for an arbitrary flow may also be reduced to a Dirichlet problem in potential theory. The Green's function for the lens is also derived and the extension of the approach to non-axially symmetric problems is considered.