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Journal Articles Calculus of Variations and Partial Differential Equations Year : 2011

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

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.

Dates and versions

hal-00660435 , version 1 (16-01-2012)

Identifiers

Cite

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