# Scalar Reduction Tchniques for Weakly Coupled Hamilton-Jacobi Systems

## TL;DR

This paper introduces scalar reduction techniques for weakly coupled Hamilton-Jacobi systems, providing algorithms for critical solutions, characterizations of Aubry set points, and semiconcavity properties.

## Contribution

It develops a novel control-theoretic algorithm for solving weakly coupled Hamilton-Jacobi systems at the critical level.

## Key findings

- Constructed an algorithm for critical solutions as limits of subsolutions.
- Characterized isolated points of the Aubry set.
- Established semiconcavity properties for critical subsolutions.

## Abstract

We study a class of weakly coupled systems of Hamilton{Jacobi equations at the critical level. We associate to it a family of scalar discounted equation. Using control{theoretic tech- niques we construct an algorithm which allows obtaining a critical solution to the system as limit of a monotonic sequence of subsolutions. We moreover get a characterization of isolated points of the Aubry set and establish semiconcavity properties for critical subsolutions.