Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations

Cardaliaguet, Pierre; Souganidis, Panagiotis E.

Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2015), Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations, Annales de l'Institut Henri Poincaré (C) Analyse non linéaire, 32, 3, p. 571-591. http://dx.doi.org/10.1016/j.anihpc.2014.01.007

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1308.3313v1

Date

2015

Journal name

Annales de l'Institut Henri Poincaré (C) Analyse non linéaire

Volume

Number

Publisher

Elsevier

Pages

571-591

Abstract (EN)

We prove that the effective nonlinearities (ergodic constants) obtained in the stochastic homogenization of Hamilton-Jacobi, “viscous” Hamilton-Jacobi and nonlinear uniformly elliptic pde are approximated by the analogous quantities of appropriate “periodizations” of the equations. We also obtain an error estimate, when there is a rate of convergence for the stochastic homogenization.

Subjects / Keywords

Hamilton–Jacobi equation; nonlinear system; stochastic homogenization