Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form

By S. Armstrong, Charles K. Smart. Archive for Rational Mechanics and Analysis, 2013

57 citations recorded by the source corpus.

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–Ampère equation.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/7120ff65bc1a7d0e981caeb268ac6a5e0a44e0dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Finance

Citations in the corpus

Quantitative stochastic homogenization of convex integral functionals (2014, result): “The analysis in the present paper was informed by some ideas from our previous work [1], which contained similar results for equations in nondivergence form.”
A higher-order large-scale regularity theory for random elliptic operators (2015, background): “In the case of fully nonlinear elliptic equations, a logarithmic rate of convergence has been established by Ca arelli and Souganidis [7] under a very weak assumption on decorrelation; Armstrong and Smart [4] have obtained a power-law rate of convergence in the case of nite range of dependence.”