Metric techniques for convex stationary ergodic Hamiltonians |
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Authors: | Andrea Davini Antonio Siconolfi |
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Affiliation: | 1. Dipartimento di Matematica, Universit?? di Roma ??La Sapienza??, P.le Aldo Moro 2, 00185, Roma, Italy
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Abstract: | We adapt the metric approach to the study of stationary ergodic Hamilton?CJacobi 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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