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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
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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
Received: 15.07.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 2, Pages 25–32
DOI: https://doi.org/10.3103/S1066369X16020055
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
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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