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

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

2009-07-30

arxiv.org/abs/0907.5332v1

Mathematics

Analysis of PDEs

31 pages

Scientific paper

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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