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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 2, Pages 31–39 (Mi ivm9079)  

The Landau–Kolmogorov problem for the Laplace operator on a ball

A. A. Koshelevab

a Chair of Mathematical Analysis and Function Theory, Ural Federal University, 19 Mira str., Ekaterinburg, 620002 Russia
b Department of Approximation Theory, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 51 Lenin ave., Ekaterinburg, 620000 Russia

Abstract: In this paper we solve the problem of maximizing the value of the Laplace operator at the origin for functions such that the second degree of the Laplace operator belongs to the space $L_\infty$ on the unit ball of the Euclidean space. The problem is solved under restrictions on the uniform norm of a function and the $L_\infty$-norm of ther second degree of the Laplace operator of this function.

Keywords: Landau–Kolmogorov problem, Landau–Kolmogorov inequality, Laplace operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-02705
Ministry of Education and Science of the Russian Federation 02.A03.21.0006


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:2, 25–32

Bibliographic databases:

UDC: 517.518
Received: 15.07.2014

Citation: A. A. Koshelev, “The Landau–Kolmogorov problem for the Laplace operator on a ball”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 2, 31–39; Russian Math. (Iz. VUZ), 60:2 (2016), 25–32

Citation in format AMSBIB
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\paper The Landau--Kolmogorov problem for the Laplace operator on a~ball
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 2
\pages 31--39
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\jour Russian Math. (Iz. VUZ)
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\vol 60
\issue 2
\pages 25--32
\crossref{https://doi.org/10.3103/S1066369X16020055}
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  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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