Geodesic
On estimates for the uniform norm of the Laplace operator of the best interpolants on a class of bounded interpolation data
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 191-196

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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. 
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     author = {S. I. Novikov},
     title = {On estimates for the uniform norm of the {Laplace} operator of the best interpolants on a class of bounded interpolation data},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {191--196},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a18/}
}
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 1, pp. 191-196. http://geodesic.mathdoc.fr/item/TIMM_2015_21_1_a18/