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

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2014年 / 214卷 / 03期

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

页码：867 / 911

页数：45

共 50 条

[1] Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form
Scott N. Armstrong
Charles K. Smart
Archive for Rational Mechanics and Analysis, 2014, 214 : 867 - 911
[2] Optimal Quantitative Estimates in Stochastic Homogenization for Elliptic Equations in Nondivergence Form
Armstrong, Scott
Lin, Jessica
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 225 (02) : 937 - 991
[3] Optimal Quantitative Estimates in Stochastic Homogenization for Elliptic Equations in Nondivergence Form
Scott Armstrong
Jessica Lin
Archive for Rational Mechanics and Analysis, 2017, 225 : 937 - 991
[4] ON THE PERIODIC HOMOGENIZATION OF ELLIPTIC EQUATIONS IN NONDIVERGENCE FORM WITH LARGE DRIFTS
Jing, Wenjia
Zhang, Yiping
MULTISCALE MODELING & SIMULATION, 2023, 21 (04): : 1486 - 1501
[5] Characterizations of diffusion matrices in homogenization of elliptic equations in nondivergence-form
Guo, Xiaoqin
Sprekeler, Timo
Tran, Hung V.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2025, 64 (01)
[6] Boundary behavior of solutions of elliptic equations in nondivergence form
Yongpan Huang
Dongsheng Li
Lihe Wang
Manuscripta Mathematica, 2014, 143 : 525 - 541
[7] Boundary behavior of solutions of elliptic equations in nondivergence form
Huang, Yongpan
Li, Dongsheng
Wang, Lihe
MANUSCRIPTA MATHEMATICA, 2014, 143 (3-4) : 525 - 541
[8] HOMOGENIZATION OF NONDIVERGENCE-FORM ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS AND FINITE ELEMENT APPROXIMATION OF THE HOMOGENIZED PROBLEM
Sprekeler, Timo
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2024, 62 (02) : 646 - 666
[9] Finite element approximation of elliptic homogenization problems in nondivergence-form
Capdeboscq, Yves
Sprekeler, Timo
Suli, Endre
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2020, 54 (04): : 1221 - 1257
[10] A note on boundary differentiability of solutions of elliptic equations in nondivergence form
Yongpan Huang
Dongsheng Li
Lihe Wang
manuscripta mathematica, 2020, 162 : 305 - 313

← 1 2 3 4 5 →