We study liquid drops lying on a rough planar surface. The drops are minimizers of an energy functional that includes a random adhesion energy. We prove the existence of minimizers and the regularity of the free boundary. When the length scale of the randomly varying surface is small, we show that minimizers are close to spherical caps which are minimizers of an averaged energy functional. In particular, we give an error estimate that is algebraic in the scale parameter and holds with high probability.
1
University of Maryland, College Park, USA
2
Duke University, Durham, USA
Antoine Mellet; James Nolen. Capillary drops on a rough surface. Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 167-184. doi: 10.4171/ifb/278
@article{10_4171_ifb_278,
author = {Antoine Mellet and James Nolen},
title = {Capillary drops on a rough surface},
journal = {Interfaces and free boundaries},
pages = {167--184},
year = {2012},
volume = {14},
number = {2},
doi = {10.4171/ifb/278},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/278/}
}
TY - JOUR
AU - Antoine Mellet
AU - James Nolen
TI - Capillary drops on a rough surface
JO - Interfaces and free boundaries
PY - 2012
SP - 167
EP - 184
VL - 14
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/278/
DO - 10.4171/ifb/278
ID - 10_4171_ifb_278
ER -
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%J Interfaces and free boundaries
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%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/278/
%R 10.4171/ifb/278
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