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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