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

Pierre Cardaliaguet (1) , Panagiotis E. Souganidis (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Chicago]

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Cardaliaguet, Panagiotis E. Souganidis. 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, 2015, 32 (3), pp.571-591. ⟨hal-00851410⟩