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Scalar reduction techniques for weakly coupled Hamilton-Jacobi systems. (English) Zbl 1415.35094

Summary: 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.

MSC:

35F21 Hamilton-Jacobi equations
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
37J50 Action-minimizing orbits and measures (MSC2010)
35D40 Viscosity solutions to PDEs
35Q93 PDEs in connection with control and optimization
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