Quantitative stochastic homogenization of convex integral functionals
Abstract
We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but suboptimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched $C^{0,1}$ estimates for local minimizers of such energy functionals.
 Publication:

arXiv eprints
 Pub Date:
 June 2014
 DOI:
 10.48550/arXiv.1406.0996
 arXiv:
 arXiv:1406.0996
 Bibcode:
 2014arXiv1406.0996A
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Probability;
 35B27;
 60H25;
 35J20;
 35J62
 EPrint:
 59 pages, revised version