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.
Scalar reduction techniques for weakly coupled Hamilton–Jacobi systems / Siconolfi, A.; Zabad, S.. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 25:6(2018). [10.1007/s00030-018-0540-8]
Scalar reduction techniques for weakly coupled Hamilton–Jacobi systems
Siconolfi A.;Zabad S.
2018
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 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.| File | Dimensione | Formato | |
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