JournalsaihpcVol. 32, No. 3pp. 571–591

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

  • Pierre Cardaliaguet

    Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France

  • Panagiotis E. Souganidis

    Department of Mathematics, University of Chicago, Chicago, IL 60637, USA
Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations cover
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Abstract

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.

Cite this article

Pierre Cardaliaguet, Panagiotis E. Souganidis, Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 3, pp. 571–591

DOI 10.1016/J.ANIHPC.2014.01.007