The Landau--Kolmogorov problem for the Laplace operator on a~ball

A. A. Koshelev

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2016), pp. 31-39.

Résumé

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.

Détail

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

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