Calculus of Variations and Geometric Measure Theory
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C. Brand - G. Dolzmann - A. Pluda

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

created by pluda on 05 Apr 2021
modified on 15 Sep 2021



Inserted: 5 apr 2021
Last Updated: 15 sep 2021

Year: 2021


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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