Calculus of Variations and Geometric Measure Theory
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A. Davini - A. Siconolfi

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

created by davini on 11 Feb 2009
modified on 17 May 2009


Accepted Paper

Inserted: 11 feb 2009
Last Updated: 17 may 2009

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.

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