Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves
Christopher Brand, Georg Dolzmann, Alessandra Pluda · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2021
Abstract 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.