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 ...

GHEENS TKOUBLE Tropical Turf Tips from the Everglades Experiment Station, Belle Glade, Fla., says: "On most courses we have visited some of the greens must be watered lightly or they become soggy, with the result that they scald under a hot sun and are readily attacked by fungus diseases. A core of sod from such greens will usually show good root growth only in the upper 2 inches and no roots a...

No. 6 at Keller Golf Course in St. Paul Although our random probing with a Hoffer tube of 142 greens on 36 golf courses back in 1969 and 1970 did work to provide documentation that just about every established green (139/142) that we sampled was infested with plant nematodes, I am not necessarily comfortable in recommending such "randomness" with regard to sampling. Plant pathogens (organisms t...