We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- 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