Plateau angle conditions for the vector-valued Allen-Cahn equation

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.

15 pages, 1 figure; minor revision, added proofs

References in corpus (2)

• Some basic facts on the system Δu - W_u (u) = 0
• Motion by Curvature of Planar Networks

Cited by in corpus (1)

• A small remark on the derivation of the plateau angle conditions for the vector-valued Allen-Cahn equation