Monotonicity and rigidity of solutions to some elliptic systems with uniform limits

Alberto Farina (1) , Berardino Sciunzi , Nicola Soave

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

In this paper, we prove the validity of Gibbons' conjecture for a coupled competing Gross-Pitaevskii system. We also provide sharp a priori bounds, regularity results and additional Liouville-type theorems.

Domaines: Mathématiques [math]

Alberto Farina, Berardino Sciunzi, Nicola Soave. Monotonicity and rigidity of solutions to some elliptic systems with uniform limits. Communications in Contemporary Mathematics, 2020, 22 (5), ⟨10.1142/S0219199719500445⟩. ⟨hal-03621404⟩