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

作者：Bellettini G; Kholmatov Sh Yu^*

来源：Journal de Mathematiques Pures et Appliquees, 2018, 117: 1-58.

DOI：10.1016/j.matpur.2018.06.003

• Mean curvature flow with prescribed contact angle
• Sets of finite perimeter
• Capillary functional
• Minimizing movements

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 solutions constructed as a limit of an approximation algorithm of Almgren-Taylor-Wang and Luckhaus-Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results.

• 出版日期2018-9