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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2011 Volume 17, Number 3, Pages 258–265 (Mi timm737)

This article is cited in 2 papers

Interpolation in a ball with a minimum value of the $L_p$-norm of the Laplace operator

S. I. Novikovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: We consider the problem of interpolating finite sets of numerical data bounded in $l_p$-norms ($1\leq p<\infty$) by smooth functions that are defined in an $n$-dimensional Euclidean ball of radius $R$ and vanish on the boundary of the ball. Under some constraints on the location of interpolation nodes, we obtain two-sided estimates with a correct dependence on $R$ for the $L_p$-norms of the Laplace operators of the best interpolants.

Keywords: interpolation, Laplace operator, cubic $B$-splines.

UDC: 517.51

Received: 27.10.2010



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