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

A. A. Koshelev<sup>ab

a</sup> 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.

UDC: 517.518

Received: 15.07.2014

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

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