Calculus of Variations and Geometric Measure Theory

A. Davini - A. Siconolfi

Exact and approximate correctors for stochastic Hamiltonians: the 1--dimensional case

created by davini on 11 Feb 2009
modified on 13 Jul 2023


Published Paper

Inserted: 11 feb 2009
Last Updated: 13 jul 2023

Journal: Math. Annalen
Year: 2009


We perform a qualitative investigation of critical Hamilton--Jacobi equations, with stationary ergodic Hamiltonian, in dimension $1$. We show the existence of approximate correctors, give characterizing conditions for the existence of correctors, provide Lax--type representation formulae and establish comparison principles. The results are applied to look into the corresponding effective Hamiltonian and to study an homogenization problem. In the analysis a crucial role is played by tools issued from stochastic geometry such as, for instance, closed random stationary sets.