On the calculation of potential function defined on curved boundaries

Abstract

The equations describing a boundary value problem for a vector field u are often equivalent to a variational principle containing an integral ƒf.δud∑ over a part ∑ of the boundary, where f is a prescribed function either of position or, more generally, of the surface values of u and its surface derivatives. In the latter case it is not obvious when such an integral can be written in the useful form δƒ D d∑ in terms of a ‘surface potential’ function D . This question is here examined in some detail from a general standpoint, with examples.