We use `p estimates together with Brascamp-Lieb inequalities to obtain bounds on the variance of the solution u" to the elliptic equation r" a(x="; ')r"u" = r" f . The variance is shown to be O("r) where the exponent r depends on the contrast of a(x; '). In two dimensions, we show that variance of the Greens function of the above elliptic operator is bounded. We also obtain decay rates for the ...
