A free boundary problem with facets
Analysis of PDEs
2018-11-14 v1
Abstract
We study a free boundary problem on the lattice whose scaling limit is a harmonic free boundary problem with a discontinuous Hamiltonian. We find an explicit formula for the Hamiltonian, prove the solutions are unique, and prove that the limiting free boundary has a facets in every rational direction. Our choice of problem presents difficulties that require the development of a new uniqueness proof for certain free boundary problems. The problem is motivated by physical experiments involving liquid drops on patterned solid surfaces.
Cite
@article{arxiv.1711.00965,
title = {A free boundary problem with facets},
author = {William M Feldman and Charles K Smart},
journal= {arXiv preprint arXiv:1711.00965},
year = {2018}
}
Comments
38 pages, 2 figures