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.
Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves
Pluda A.
2023-01-01
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.File in questo prodotto:
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Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves.pdf
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