On the confinement of bounded entire solutions to a class of semilinear elliptic systems

TL;DR

This paper proves that bounded solutions to certain semilinear elliptic systems are confined within convex domains and establishes a Liouville type theorem for strictly convex domains, extending previous results with weaker assumptions.

Contribution

It extends existing confinement and Liouville theorems for semilinear elliptic systems under less regularity assumptions.

Findings

Bounded solutions are confined in convex domains.

Liouville theorem holds for strictly convex domains.

Results apply to various applications.

Abstract

Under appropriate assumptions, we show that all bounded entire solutions to a class of semilinear elliptic systems are confined in a convex domain. Moreover, we prove a Liouville type theorem in the case where the domain is strictly convex. Our result represents an extension, under less regularity assumptions, of a recent result of Smyrnelis. We also provide several applications.