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

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Brand, Christopher ; Dolzmann, Georg ; Pluda, Alessandra
License: Creative Commons Attribution Non-commercial No Derivatives 4.0
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Date of publication of this fulltext: 01 Dec 2021 07:39

This publication is part of the DEAL contract with Wiley.


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.

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