Journal
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
Volume 38, Issue 2, Pages 304-338Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03605302.2012.715319
Keywords
Fluctuation; Quantification of uncertainty; Stochastic homogenization; Stochastic perturbation; Variance estimate; 35B27; 35J15; 39A70; 60H25; 60F99
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We consider a linear elliptic equation in divergence form on a bounded domain (or on R d ) in dimension d = 2, whose coefficients are perturbed by a stationary noise of correlation length ? > 0. We give estimates on the fluctuation of the solution in function of the correlation length ? of the noise, both in terms of strong L 2 and weak L 1 norms. This result can be seen as a quantification of the propagation of uncertainties in linear elliptic partial differential equations.
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