Metric techniques for convex stationary ergodic Hamiltonians

Davini, Andrea; Siconolfi, Antonio
March 2011
Calculus of Variations & Partial Differential Equations;Mar2011, Vol. 40 Issue 3/4, p391
Academic Journal
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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