Interpolation by functions from a Sobolev space with minimum L-p-norm of the Laplace operator

被引：0
|
作者：
Novikov, S., I
机构：
来源：
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2015年 / 21卷 / 04期
关键词：
interpolation; Laplace operator; Sobolev space; embedding;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider an interpolation problem with minimum value of the L-p-norm (1 <= p < infinity) of the Laplace operator of interpolants for a class of interpolated sequences that are bounded in the l(p)-norm. The data are interpolated at nodes of the grid formed by points from R-n with integer coordinates. It is proved that, if 1 <= p < n/2, then the L-p-norm of the Laplace operator of the interpolant can be arbitrarily small for any sequence that is interpolated. Two-sided estimates for the L-2-norm of the Laplace operator of the best interpolant are found for the case n = 2.
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页码：212 / 222
页数：11
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