Anisotropic Surface Tensions for Phase Transitions in Periodic Media
Analysis of PDEs
2021-08-24 v2 Mathematical Physics
Metric Geometry
math.MP
Abstract
This paper establishes bounds on the homogenized surface tension for a heterogeneous Allen-Cahn energy functional in a periodic medium. The approach is based on relating the homogenized energy to a purely geometric variational problem involving the large scale behaviour of the signed distance function to a hyperplane in periodic media. Motivated by this, a homogenization result for the signed distance function to a hyperplane in both periodic and almost periodic media is proven.
Keywords
Cite
@article{arxiv.2010.05849,
title = {Anisotropic Surface Tensions for Phase Transitions in Periodic Media},
author = {Rustum Choksi and Irene Fonseca and Jessica Lin and Raghavendra Venkatraman},
journal= {arXiv preprint arXiv:2010.05849},
year = {2021}
}
Comments
Fixed an error in an earlier version and other revisions. 40 pages