Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form

被引:24
|
作者
Armstrong, Scott N. [1 ]
Smart, Charles K. [2 ]
机构
[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris, France
[2] MIT, Dept Math, Cambridge, MA 02139 USA
关键词
PARTIAL-DIFFERENTIAL-EQUATIONS; VISCOSITY SOLUTIONS; MEDIA;
D O I
10.1007/s00205-014-0765-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a finite range of dependence. The results are new even for linear equations. The arguments rely on a new geometric quantity which is controlled in part by adapting elements of the regularity theory for the Monge-AmpSre equation.
引用
收藏
页码:867 / 911
页数:45
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