Convergence of a minimizing movement scheme for contact-angle mean curvature flow in a smooth bounded domain
Year: 2026
Type: preprint
Abstract: This paper studies a Chambolle-type minimizing movement scheme for mean curvature flow with prescribed contact angle in a smooth bounded domain. The scheme is based on the capillary functional and the geodesic signed distance relative to the container, and yields a time-discrete level-set approximation. The main result asserts that, for every Lipschitz-continuous boundary function prescribing a strictly nondegenerate contact angle, the approximate solutions converge locally uniformly to the unique viscosity solution of the corresponding level-set mean curvature equation with oblique derivative boundary condition. This improves a previous convergence theorem, where the container was assumed to be convex and a curvature-type condition relating the tangential derivative of the prescribed contact-angle function to the principal curvatures of the container boundary was imposed. The main new ingredient is a uniform Lipschitz estimate for the solutions of the variational problems defining the scheme. This estimate is derived by applying a Bernstein-type argument to a suitable weighted gradient, rather than to the gradient itself, which rules out boundary maxima without relying on the previous curvature-type condition.
Source: arXiv (Cornell University)
Authors: Eto, Tokuhiro, Jang, Jiwoong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167012853