Hardy inequality and Lp estimates for the torsion function
Hardy inequality and Lp estimates for the torsion function
复制标题
扭转函数的 Hardy 不等式和 Lp 估计
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
T. Carroll
中科院分区：
文献类型：
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作者：
M. V. D. van den Berg;T. Carroll
证明了欧氏空间中开集D的挠函数在L∞（D）中当且仅当D中Dirichlet Laplacian的谱远离0有界.对于1 <$p <$∞，证明了当到边界函数的距离在L2 p（D）中时，如果作用在L2（D）中的Dirichlet Laplacian满足强哈代不等式，则D的挠函数精确地在Lp（D）中.
It is shown that the torsion function for an open set D in Euclidean space ℝm is in L∞(D) if and only if the spectrum of the Dirichlet Laplacian in D is bounded away from 0. For 1 ⩽ p ⩽ ∞, it is shown that the torsion function for D is in Lp(D) precisely when the distance to the boundary function is in L2p(D), if it is assumed that the Dirichlet Laplacian acting in L2(D) satisfies a strong Hardy inequality.