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

Andrea Davini; Antonio Siconolfi

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arXiv · 0907.5332

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

Andrea Davini·Antonio Siconolfi

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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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Andrea Davini, Antonio Siconolfi. 2009-07-30. A metric analysis of critical Hamilton--Jacobi equations in the stationary ergodic setting. https://arxiv.org/abs/0907.5332

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