Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited

Smart, Charles K.; Armstrong, Scott N.

Smart, Charles K.; Armstrong, Scott N. (2014), Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited, Calculus of Variations and Partial Differential Equations, 50, 3-4, p. 967-980. http://dx.doi.org/10.1007/s00526-013-0663-z

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/1209.4741

Date

2014

Journal name

Calculus of Variations and Partial Differential Equations

Volume

Number

3-4

Publisher

Springer

Pages

967-980

Abstract (EN)

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.

Subjects / Keywords

fully nonlinear elliptic equation; stochastic homogenization