Abstract
We consider potentials Gk μ associated with the Weinstein equation with parameter k in ℝ, Σj=1n (∂2u/∂ x2j) + (k/xn) (∂ u/∂ xn) = 0, on the upper half space in ℝn. We show that if the representing measure μ satisfies the growth condition ∫ ynω/(1+|y|)n-k < ∞, where max(k, 2 − n) < ω ≤ 1, then Gk μ has a minimal fine limit of 0 at every boundary point except for a subset of vanishing (n − 2 + ω) dimensional Hausdorff measure. We also prove this exceptional set is best possible.
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