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Stochastic homogenization of Hamilton-Jacobi equations in stationary ergodic spatio-temporal media. (English) Zbl 1180.35082
This paper is devoted to the homogenization process of a class of convex Hamilton-Jacobi equations in spatio-temporal stationary ergodic media. The main obstruction to proving homogenization results for this problem, with respect to time and space variables simultaneously, is the lack of a priori regularity of the solutions; this difficulty is overcome here. The author considers a perturbed problem with an appropriate Hamiltonian, for which the homogenization is performed by already known methods. The properties of the homogenized approximating problem complete the study.

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
47A35 Ergodic theory of linear operators
35F21 Hamilton-Jacobi equations
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