Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited
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Author(s)
Armstrong, Scott N
Smart, Charles
Date Issued
September 2013
Journal
Calculus of Variations and Partial Differential Equations
Publisher
Springer-Verlag
Citation
Armstrong, Scott N., and Charles K. Smart. “Stochastic Homogenization of Fully Nonlinear Uniformly Elliptic Equations Revisited.” Calculus of Variations and Partial Differential Equations, Vol. 50, no. 3–4 (September 2013), pp. 967–980.
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Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00526-013-0663-z
