# Critical Chirality in Elliptic Systems

## TL;DR

This paper proves regularity results for solutions to certain critical elliptic systems in two dimensions, involving involution operators with finite energy, advancing understanding of their mathematical properties.

## Contribution

It establishes the regularity of $L^2$ solutions to critical elliptic systems with involution operators in divergence form in two dimensions.

## Key findings

- Proves regularity of solutions in 2D for specific elliptic systems.
- Handles systems involving involution operators with finite energy.
- Advances mathematical understanding of critical elliptic systems.

## Abstract

We establish the regularity in 2 dimensions of $L^2$ solutions to critical elliptic systems in divergence form involving involution operators of finite $W^{1,2}$-energy.