Calculus of Variations and Geometric Measure Theory

A. Davini - A. Siconolfi

Metric techniques for convex stationary ergodic Hamiltonians

created by davini on 12 Jul 2023
modified on 13 Jul 2023


Published Paper

Inserted: 12 jul 2023
Last Updated: 13 jul 2023

Journal: Calc. Var. Partial Differential Equations
Volume: 40
Number: 3-4
Pages: 391–421
Year: 2011

ArXiv: 0907.5332 PDF


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 existencenonexistence of exact or approximate critical admissible solutions.