Inserted: 29 may 2017
Last Updated: 29 may 2017
We discuss the local minimality of some configurations for a functional involving fractional perimeter and a prescribed curvature term. We show that critical configurations with positive second variation are L1-local minimizers of our functional. Then we prove that we can obtain a sequence of L1-minimizers for the fractional Allen– Cahn energy, knowing an isolated L1-minimizer of its Gamma-limit. Finally we find minimizers for the fractional Allen–Cahn energy starting from critical configurations with positive second variation.