A remark on a surprising result by Bourgain in homogenization

In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on Zd with random coefficients in a perturbative regime using tools from harmonic analysis. This result is surprising for it goes beyond the expected accuracy suggested by recent results in quantitative stochastic homogenization. In this short article we reformulate Bourgain’s result in a form that highlights its interest to the state-of-the-art in homogenization (and especially the theory of fluctuations), and we state several related conjectures.


Published in:
Communications in Partial Differential Equations, 44, 12, 1345-1357
Year:
Dec 02 2019
ISSN:
0360-5302
1532-4133
Laboratories:




 Record created 2020-10-01, last modified 2020-10-01


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