A metric analysis of critical Hamilton--Jacobi equations in the stationary ergodic setting

Andrea Davini 1 Antonio Siconolfi 1
1 Sapienza University of Rome - Dipartimento di Matematica "Guido Castelnuovo" [Roma I]
Abstract : We adapt the metric approach to the study of stationary ergodic Hamilton-Jacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Hamiltonian greater than or equal to a distinguished critical value, we define an intrinsic random semidistance and prove that an asymptotic norm does exist. Taking as source region a suitable class of closed random sets, we show that the Lax formula provides admissible subsolutions. This enables us to relate the degeneracies of the critical stable norm to the existence/nonexistence of exact or approximate critical admissible solutions.
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Calculus of Variations and Partial Differential Equations, Springer Verlag, 2011, 40 (3-4), pp.391-421. 〈10.1007/s00526-010-0345-z〉
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https://hal.inria.fr/hal-00660435
Contributeur : Estelle Bouzat <>
Soumis le : lundi 16 janvier 2012 - 16:20:25
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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Andrea Davini, Antonio Siconolfi. A metric analysis of critical Hamilton--Jacobi equations in the stationary ergodic setting. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2011, 40 (3-4), pp.391-421. 〈10.1007/s00526-010-0345-z〉. 〈hal-00660435〉

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