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arXiv · 2602.07989

Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions

Linlin Fan·Peibiao Zhao
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Abstract

Wang, Weng and Xia[Math. Ann. 388 (2024), no. 2] studied a mean curvature type flow for the smooth, embedded capillary hypersurfaces with a constant contact angle $\theta\in(0,\pi)$ and confirmed the existence of solutions by the standard PDE theory. In the present paper, we study a fractional mean curvature flow for $C^{1,1}$-regular hypersurfaces with a capillary-type boundary condition and obtain the short time existence by the fixed point argument.

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Linlin Fan, Peibiao Zhao. 2026-02-08. Existence of the classical solution to the fractional mean curvature flow with capillary-type boundary conditions. https://arxiv.org/abs/2602.07989

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