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

Variational models for the interaction of surfactants with curvature -- existence and regularity of minimizers in the case of flexible curves