We study a class of weakly coupled Hamilton–Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing the Lagrangians obtained by duality from the Hamiltonians of the system. We use them to characterize, by means of a suitable estimate, all the subsolutions of the system, and to explicitly represent some subsolutions enjoying an additional maximality property. A crucial step for our analysis is to put the problem in a suitable random frame. Only some basic knowledge of measure theory is required, and the presentation is accessible to readers without background in probability.
A lagrangian approach to weakly coupled Hamilton-Jacobi systems / Siconolfi, Antonio; H., ioyoshi Mitake; Hang V., Tran; N., aoki Yamada. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - (2016), pp. 821-846. [10.1137/15M1010841]
A lagrangian approach to weakly coupled Hamilton-Jacobi systems
SICONOLFI, Antonio;
2016
Abstract
We study a class of weakly coupled Hamilton–Jacobi systems with a specific aim to perform a qualitative analysis in the spirit of weak KAM theory. Our main achievement is the definition of a family of related action functionals containing the Lagrangians obtained by duality from the Hamiltonians of the system. We use them to characterize, by means of a suitable estimate, all the subsolutions of the system, and to explicitly represent some subsolutions enjoying an additional maximality property. A crucial step for our analysis is to put the problem in a suitable random frame. Only some basic knowledge of measure theory is required, and the presentation is accessible to readers without background in probability.File | Dimensione | Formato | |
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