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

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.

preprint2013arXivOpen access
Pierre CardaliaguetPanagiotis E. Souganidis
math.AP
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Pierre CardaliaguetPanagiotis E. Souganidis

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