BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness

Sebastian Hensel; Tim Laux

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arXiv · 2112.11150

BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness

Sebastian Hensel·Tim Laux

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Abstract

We study weak solutions to mean curvature flow satisfying Young's angle condition for general contact angles $\alpha \in (0,\pi)$. First, we construct BV solutions using the Allen-Cahn approximation with boundary contact energy as proposed by Owen and Sternberg. Second, we prove the weak-strong uniqueness and stability for this solution concept. The main ingredient for both results is a relative energy, which can also be interpreted as a tilt excess.

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Sebastian Hensel, Tim Laux. 2021-12-21. BV solutions for mean curvature flow with constant contact angle: Allen-Cahn approximation and weak-strong uniqueness. https://arxiv.org/abs/2112.11150

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