The 3G inequality for a uniformly John domain
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概要
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Let <I>G</I> be the Green function for a domain <I>D</I>⊂<B>R</B><SUP><I>d</I></SUP> with <I>d</I>≥3. The Martin boundary of <I>D</I> and the 3G inequality:<BR>\frac{<I>G</I>(<I>x</I>, <I>y</I>)<I>G</I>(<I>y</I>, <I>z</I>)}{<I>G</I>(<I>x</I>, <I>z</I>)}≤<I>A</I>(<I>|x</I>−<I>y|</I><SUP>2−<I>d</I></SUP>+<I>|y</I>−<I>z|</I><SUP>2−<I>d</I></SUP>) for <I>x</I>, <I>y</I>, <I>z</I>∈<I>D</I><BR>are studied. We give the 3G inequality for a bounded uniformly John domain <I>D</I>, although the Martin boundary of <I>D</I> need not coincide with the Euclidean boundary. On the other hand, we construct a bounded domain such that the Martin boundary coincides with the Euclidean boundary and yet the 3G inequality does not hold.
- 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文
国立大学法人 東京工業大学大学院理工学研究科数学専攻 | 論文
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