Minimizing movements for mean curvature flow of droplets with prescribed   contact angle
  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. 
Giovanni Bellettini, Shokhrukh Yusufovich Kholmatov
math.AP