Abstract
AbstractLet Ω be a proper subdomain of ℝn, n ≥ 2, and let x0∈ Ω be fixed. By GΩ and KΩ we denote the Green function and the Martin kernel for Ω, respectively. Under a certain assumption on Ω near a boundary point ξ, we show that the product GΩ(x, x0)KΩ(x, ξ) is comparable to |x - ξ|2-n for x in a nontangential cone with vertex at ξ. We also give an estimate for the product KΩ(x, ξ)KΩ(x,η) in a uniform domain, where η is another boundary point.
Publisher
Cambridge University Press (CUP)
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