Unit density of the limiting Brakke flow

Determine whether the Brakke flows obtained as limits of the vector-valued Allen–Cahn systems with the paper’s specially designed discrete-well potentials have unit density.

Background

The main theorem establishes that subsequential limits of the Allen–Cahn energy measures are rectifiable Brakke flows. The partial regularity theory cited in the paper, however, requires unit density of the Brakke flow.

The authors do not prove unit density for their limiting flows and identify this property as an unresolved issue for future work. Establishing it would allow the available regularity results for unit-density Brakke flows to be applied directly to the limits constructed in the paper.