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arXiv · 2011.12632

Lower regularity assumption for an Euler-Lagrange equation on the contact line of the phase dependent Helfrich energy

Sascha Eichmann
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Abstract

We examine the phase dependent Helfrich energy and show an Euler-Lagrange equation on the phase seperation line. This result has already been observed by e.g. J\"ulicher-Lipowski and later Elliot-Stinner. Here we are able to lower the regularity assumption for this result down to $C^{1,1}$ for the seperation line. In the proof we employ a carefully choosen test function utilising the signed distance function.

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Sascha Eichmann. 2020-11-25. Lower regularity assumption for an Euler-Lagrange equation on the contact line of the phase dependent Helfrich energy. https://arxiv.org/abs/2011.12632

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