Scalar reduction techniques for weakly coupled Hamilton–Jacobi systems

  • Antonio SiconolfiEmail author
  • Sahar Zabad


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.


Weakly coupled systems Hamilton–Jacobi equations Viscosity solutions Aubry set Optimal control Critical value 

Mathematics Subject Classification

35F21 49L25 37J50 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Rome “La Sapienza”RomeItaly

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