Minimizing movements for mean curvature flow of droplets with prescribed contact angle

TL;DR

This paper investigates the evolution of droplets under mean curvature flow with a prescribed contact angle, establishing existence and comparison results for weak solutions using the minimizing movements method.

Contribution

It introduces a novel application of the minimizing movements method to mean curvature flow with nonconstant contact angles, ensuring weak solution existence and compatibility.

Findings

Existence of weak evolution for droplet flow

Compatibility with distributional solutions

Comparison results for solutions

Abstract

We study the mean curvature motion of a droplet flowing by mean curvature on a horizontal hyperplane with a possibly nonconstant prescribed contact angle. Using the minimizing movements method we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results.