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

## TL;DR

This paper proves Gibbons' conjecture for a coupled Gross-Pitaevskii system, establishing key properties like monotonicity, rigidity, and regularity, along with sharp bounds and Liouville-type theorems.

## Contribution

It extends the understanding of elliptic systems by confirming Gibbons' conjecture and providing new bounds and regularity results for solutions.

## Key findings

- Validation of Gibbons' conjecture for the system
- Establishment of sharp a priori bounds and regularity
- Derivation of Liouville-type theorems

## Abstract

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.