Title: A Free Boundary Problem with Facets.
Authors: Feldman, William M.; Smart, Charles K.
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 that 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.
Subjects: BOUNDARY value problems; HAMILTONIAN systems; LATTICE theory; UNIQUENESS (Mathematics); DROPLETS
Publication: Archive for Rational Mechanics & Analysis, 2019, Vol 232, Issue 1, p389
ISSN: 0003-9527
Publication type: Academic Journal
DOI: 10.1007/s00205-018-1323-4

A Free Boundary Problem with Facets.

Feldman, William M.; Smart, Charles K.