Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

• Main Authors: Armstrong, Scott N (Author), Smart, Charles (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Springer-Verlag, 2016-10-19T17:33:51Z.
• Subjects: Article
• Online Access: Get fulltext

We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of estimates for the first derivatives of approximate correctors by modifying the perturbed test function argument to take advantage of the spreading of the contact set.
National Science Foundation (U.S.) (DMS-1004645)
National Sicence Foundation (U.S.) (DMS-1004595)
Chaire Junior of la Fondation Sciences Mathématiques de Paris