scholarly journals Optimal Quantitative Estimates in Stochastic Homogenization for Elliptic Equations in Nondivergence Form

2017 ◽  
Vol 225 (2) ◽  
pp. 937-991 ◽  
Author(s):  
Scott Armstrong ◽  
Jessica Lin
Keyword(s):  
Elliptic Equations ◽  
Stochastic Homogenization ◽  
Nondivergence Form ◽  
Quantitative Estimates

On weighted W2,p estimates for elliptic equations with BMO coefficients in nondivergence form

2015 ◽  
Vol 26 (01) ◽  
pp. 1550001 ◽  
Author(s):  
Sun-Sig Byun ◽  
Mikyoung Lee
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nondivergence Form ◽  
Muckenhoupt Class ◽  
The Matrix ◽  
Bmo Coefficients

We establish global weighted W2,p, 2 < p < ∞, estimates for the solution to the Dirichlet problem for an elliptic equation in nondivergence form with BMO coefficients in a C1,1 domain under the assumption that the matrix of the coefficients has a small BMO semi-norm while the associated weight belongs to a Muckenhoupt class. These conditions are weaker than those reported in the literature.

scholarly journals Special quasirandom structures: A selection approach for stochastic homogenization

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Claude Le Bris ◽  
Frédéric Legoll ◽  
William Minvielle
Keyword(s):  
Solid State ◽  
Elliptic Equations ◽  
Variance Reduction ◽  
Divergence Form ◽  
Atomistic Simulations ◽  
Stochastic Homogenization ◽  
Selection Approach ◽  
Reduction Approach

AbstractWe adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science

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