Geodesic
Minimizing movements for forced anisotropic curvature flow of droplets
Shokhrukh Kholmatov1 orcid
1University of Vienna, Austria
Interfaces and free boundaries, Tome 27 (2025) no. 3, pp. 349-402

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DOI

We study forced anisotropic curvature flow of droplets on an inhomogeneous horizontal hyperplane. As in Bellettini and Kholmatov [J. Math. Pures Appl. 117 (2018), 1–58], 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.
DOI : 10.4171/ifb/529
Classification : 53E10, 49Q20, 35A15, 35D30, 35D35
Mots-clés : anisotropy, capillarity functional, droplet, anisotropic curvature flow, minimizing movements, consistency

Shokhrukh Kholmatov  1

1 University of Vienna, Austria 
Shokhrukh Kholmatov. Minimizing movements for forced anisotropic curvature flow of droplets. Interfaces and free boundaries, Tome 27 (2025) no. 3, pp. 349-402. doi: 10.4171/ifb/529
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     title = {Minimizing movements for forced anisotropic curvature flow of droplets},
     journal = {Interfaces and free boundaries},
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     year = {2025},
     volume = {27},
     number = {3},
     doi = {10.4171/ifb/529},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/529/}
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