### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 867-911 |

Number of pages | 45 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 214 |

Issue number | 3 |

DOIs | |

State | Published - Oct 17 2014 |

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### ASJC Scopus subject areas

- Analysis
- Mechanical Engineering
- Mathematics (miscellaneous)

### Cite this

*Archive for Rational Mechanics and Analysis*,

*214*(3), 867-911. https://doi.org/10.1007/s00205-014-0765-6

**Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form.** / Armstrong, Scott; Smart, Charles K.

Research output: Contribution to journal › Article

*Archive for Rational Mechanics and Analysis*, vol. 214, no. 3, pp. 867-911. https://doi.org/10.1007/s00205-014-0765-6

}

TY - JOUR

T1 - Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form

AU - Armstrong, Scott

AU - Smart, Charles K.

PY - 2014/10/17

Y1 - 2014/10/17

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84919845323&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919845323&partnerID=8YFLogxK

U2 - 10.1007/s00205-014-0765-6

DO - 10.1007/s00205-014-0765-6

M3 - Article

VL - 214

SP - 867

EP - 911

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 3

ER -