@article {BELLETTINI20181,
	title = {Minimizing movements for mean curvature flow of droplets with prescribed contact angle},
	journal = {Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
	volume = {117},
	year = {2018},
	pages = {1 - 58},
	abstract = {<p>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{\textendash}Taylor{\textendash}Wang and Luckhaus{\textendash}Sturzenhecker, we show the existence of a weak evolution, and its compatibility with a distributional solution. We also prove various comparison results. R{\'e}sum{\'e} Nous {\'e}tudions le mouvement par courbure moyenne d{\textquoteright}une goutte qui glisse par courbure moyenne sur un hyperplan horizontal avec un angle de contact prescrit {\'e}ventuellement non constant. En utilisant les solutions construites comme limites d{\textquoteright}un algorithme d{\textquoteright}approximation d{\^u} {\`a} Almgren, Taylor et Wang et Luckhaus et Sturzenhecker, nous montrons l{\textquoteright}existence d{\textquoteright}une {\'e}volution faible, et sa compatibilit{\'e} avec une solution au sens des distributions. Nous d{\'e}montrons {\'e}galement plusieurs r{\'e}sultats de comparaison.</p>},
	keywords = {Capillary functional, Mean curvature flow with prescribed contact angle, Minimizing movements, Sets of finite perimeter},
	issn = {0021-7824},
	doi = {https://doi.org/10.1016/j.matpur.2018.06.003},
	url = {http://www.sciencedirect.com/science/article/pii/S0021782418300825},
	author = {Giovanni Bellettini and Matteo Novaga and Shokhrukh Kholmatov}
}
