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

Cardaliaguet, Pierre; Souganidis, Panagiotis E.

doi:10.1016/j.anihpc.2014.01.007

Cardaliaguet, Pierre ; Souganidis, Panagiotis E.

Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 571-591.

Résumé

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.

MR Zbl

DOI : 10.1016/j.anihpc.2014.01.007

@article{AIHPC_2015__32_3_571_0,
     author = {Cardaliaguet, Pierre and Souganidis, Panagiotis E.},
     title = {Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {571--591},
     publisher = {Elsevier},
     volume = {32},
     number = {3},
     year = {2015},
     doi = {10.1016/j.anihpc.2014.01.007},
     mrnumber = {3353701},
     zbl = {1320.35040},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2014.01.007/}
}

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Cardaliaguet, Pierre; Souganidis, Panagiotis E. Periodic approximations of the ergodic constants in the stochastic homogenization of nonlinear second-order (degenerate) equations. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 571-591. doi : 10.1016/j.anihpc.2014.01.007. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.01.007/

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