# Sectional symmetry of solutions of elliptic systems in cylindrical domains

## TL;DR

This paper proves rotational symmetry for solutions of semilinear elliptic systems in cylindrical domains, especially for low-Morse index solutions under convexity conditions, extending previous symmetry results.

## Contribution

It introduces new symmetry theorems for elliptic systems in cylindrical domains, broadening the class of solutions with proven symmetry properties.

## Key findings

- Symmetry holds for low-Morse index solutions.
- Results apply under convexity assumptions on nonlinearities.
- Extends previous symmetry theorems in the literature.

## Abstract

In this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in \cite{DaPaSys, DaGlPa1, Pa, PaWe}.