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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 1, Pages 191–196 (Mi timm1155)  
On estimates for the uniform norm of the Laplace operator of the best interpolants on a class of bounded interpolation data

S. I. Novikovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
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Abstract: We consider an interpolation problem with minimum value of the uniform norm of the Laplace operator of interpolants for a class of bounded interpolated sequences. The data are interpolated at nodes of the grid formed by points from $\mathbb{R}^2$ with integer coordinates. Two-sided estimates for the uniform norm of the best interpolant are found, which improve known estimates.
Keywords: interpolation; Laplace operator; $ZP$-element.
Received: 09.11.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2016, Volume 292, Issue 1, Pages 238–244
DOI: https://doi.org/10.1134/S0081543816020206
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: S. I. Novikov, “On estimates for the uniform norm of the Laplace operator of the best interpolants on a class of bounded interpolation data”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 1, 2015, 191–196; Proc. Steklov Inst. Math. (Suppl.), 292, suppl. 1 (2016), 238–244
Citation in format AMSBIB
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\jour Proc. Steklov Inst. Math. (Suppl.)
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