Plateau angle conditions for the vector-valued Allen-Cahn equation
Analysis of PDEs
2014-04-04 v2
Abstract
Under proper hypotheses, we rigorously derive the Plateau angle conditions at triple junctions of diffused interfaces in three dimensions, starting from the vector-valued Allen-Cahn equation with a triple-well potential. Our derivation is based on an application of the divergence theorem using the divergence-free form of the equation via an associated stress tensor.
Cite
@article{arxiv.1210.0231,
title = {Plateau angle conditions for the vector-valued Allen-Cahn equation},
author = {Nicholas D. Alikakos and Panagiotis Antonopoulos and Apostolos Damialis},
journal= {arXiv preprint arXiv:1210.0231},
year = {2014}
}
Comments
15 pages, 1 figure; minor revision, added proofs