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- W2085186189 abstract "We consider a random, uniformly elliptic coefficient field $$a(x)$$ on the $$d$$ -dimensional integer lattice $$mathbb {Z}^d$$ . We are interested in the spatial decay of the quenched elliptic Green function $$G(a;x,y)$$ . Next to stationarity, we assume that the spatial correlation of the coefficient field decays sufficiently fast to the effect that a logarithmic Sobolev inequality holds for the ensemble $$langle cdot rangle $$ . We prove that all stochastic moments of the first and second mixed derivatives of the Green function, that is, $$langle |nabla _x G(x,y)|^prangle $$ and $$langle |nabla _xnabla _y G(x,y)|^prangle $$ , have the same decay rates in $$|x-y|gg 1$$ as for the constant coefficient Green function, respectively. This result relies on and substantially extends the one by Delmotte and Deuschel (Probab Theory Relat Fields 133:358–390, 2005), which optimally controls second moments for the first derivatives and first moments of the second mixed derivatives of $$G$$ , that is, $$langle |nabla _x G(x,y)|^2rangle $$ and $$langle |nabla _xnabla _y G(x,y)|rangle $$ . As an application, we are able to obtain optimal estimates on the random part of the homogenization error even for large ellipticity contrast." @default.
- W2085186189 created "2016-06-24" @default.
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- W2085186189 date "2014-11-25" @default.
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- W2085186189 title "Annealed estimates on the Green function" @default.
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- W2085186189 doi "https://doi.org/10.1007/s00440-014-0598-0" @default.
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