Scalar reduction techniques for weakly coupled Hamilton–Jacobi systems
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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 techniques 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.