Anisotropic Surface Tensions for Phase Transitions in Periodic Media
Rustum Choksi, Irene Fonseca, W. Marston Linehan, Raghavendra Venkatraman · arXiv (Cornell University) · 2020
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.