  Existence and regularity of minimizers for a geometric variational problem is
shown. The variational integral models an energy contribution of the interface
between two immiscible fluids in the presence of surfactants and includes a
Helfrich type contribution, a Frank type contribution and a coupling term
between the orientation of the surfactants and the curvature of the interface.
Analytical results are proven in a one--dimensional situation for curves.

Analysis of PDEs;Optimization and Control