Geodesic
Interpolation in a~ball with a~minimum value of the $L_p$-norm of the Laplace operator
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 258-265

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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.
Mots-clés : interpolation
Keywords: Laplace operator, cubic $B$-splines. 
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     title = {Interpolation in a~ball with a~minimum value of the $L_p$-norm of the {Laplace} operator},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a24/}
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S. I. Novikov. Interpolation in a~ball with a~minimum value of the $L_p$-norm of the Laplace operator. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 258-265. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a24/