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arXiv · 2403.09902

Minimizing movements for forced anisotropic curvature flow of droplets

Shokhrukh Yu. Kholmatov
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Abstract

We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in [Bellettini, Kholmatov: J. Math. Pures Appl. (2018)] we establish the existence of smooth flow, starting from a regular droplet and satisfying the prescribed anisotropic Young's law, and also the existence of a $1/2$-H\"older continuous in time minimizing movement solution starting from a set of finite perimeter. Furthermore, we investigate various properties of minimizing movements, including comparison principles, uniform boundedness and the consistency with the smooth flow.

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Shokhrukh Yu. Kholmatov. 2024-03-14. Minimizing movements for forced anisotropic curvature flow of droplets. https://arxiv.org/abs/2403.09902

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