Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system

Abstract

We prove the monotonicity and one-dimensional symmetry of solutions to non-cooperative fractional elliptic systems with uniform limits. In particular, our result holds for phase transitions for the fractional elliptic Gross-Pitaevskii system. The main tool we use is a sliding method adapted to fractional elliptic systems.