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Publication 21-CNA-012

Anisotropic Surface Tensions For Phase Transitions In Periodic Media

Rustum Choksi
Department of Mathematics and Statistics
McGill University
Montreal, Canada
rustum.choksi@mcgill.ca

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Jessica Lin
Department of Mathematics and Statistics
McGill University
Montreal, Canada
jessica.lin@mcgill.ca

Raghavendra Venkatraman
Courant Institute of Mathematical Sciences
New York, NY
raghav@cims.nyu.edu

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.

Get the paper in its entirety as 21-CNA-012.pdf

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