### Abstract

We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched C^{0,1} estimates for local minimizers of such energy functionals.

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

Pages (from-to) | 423-481 |

Number of pages | 59 |

Journal | Annales Scientifiques de l'Ecole Normale Superieure |

Volume | 49 |

Issue number | 2 |

State | Published - 2016 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Annales Scientifiques de l'Ecole Normale Superieure*,

*49*(2), 423-481.

**Quantitative stochastic homogenization of convex integral functionals.** / Armstrong, Scott; Smart, Charles K.

Research output: Contribution to journal › Article

*Annales Scientifiques de l'Ecole Normale Superieure*, vol. 49, no. 2, pp. 423-481.

}

TY - JOUR

T1 - Quantitative stochastic homogenization of convex integral functionals

AU - Armstrong, Scott

AU - Smart, Charles K.

PY - 2016

Y1 - 2016

N2 - We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched C0,1 estimates for local minimizers of such energy functionals.

AB - We present quantitative results for the homogenization of uniformly convex integral functionals with random coefficients under independence assumptions. The main result is an error estimate for the Dirichlet problem which is algebraic (but sub-optimal) in the size of the error, but optimal in stochastic integrability. As an application, we obtain quenched C0,1 estimates for local minimizers of such energy functionals.

UR - http://www.scopus.com/inward/record.url?scp=85007107303&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007107303&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 423

EP - 481

JO - Annales Scientifiques de l'Ecole Normale Superieure

JF - Annales Scientifiques de l'Ecole Normale Superieure

SN - 0012-9593

IS - 2

ER -