Variational methods for boundary value problems with boundary conditions appearing naturally
by
Graeme C. Wake
University of Canterbury
Coauthors: Bernie Tsang (University of Canterbury), Steve Taylor (University of Auckland)

The variational formulation of boundary value problems has been valuable in providing remarkably easy computational algorithms. In addition it provides alternative framework to use to prove existence results. Boundary conditions provide additional constraints if they need to be imposed as essential boundary conditions. The open question then is: what is the most general boundary value provblem that can be expressed in variational form with the boundary conditions appearing naturally? Special cases of two-point problems in one-dimension and some higher dimensional problems are addressed (see Tsang, B., M.Sc. thesis, University of Auckland, 1999).

There is a deep connection with self-adjointness for the linear case. The more general question remains.

Date received: September 2, 1999