Calculus of Variations and Geometric Measure Theory

S. Kholmatov

Minimizing movements for forced anisotropic curvature flow of droplets

created by kholmatov2 on 14 Mar 2024



Inserted: 14 mar 2024
Last Updated: 14 mar 2024

Year: 2024


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 $1/2$-Hölder 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.

Tags: GeMeThNES
, GeoMeG