Open AccessProperties of extrema of estimates for middle derivatives of odd order in Sobolev classes
Author(s) -
T. A. Garmanova,
I. A. Sheipak
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524875487-492
Subject(s) - sobolev space , embedding , maxima and minima , mathematics , order (exchange) , constant (computer programming) , pure mathematics , combinatorics , mathematical analysis , computer science , finance , artificial intelligence , economics , programming language
The embedding constants for the Sobolev spaces W2n[0;1]→W∞k[0; 1], 0 ≤ k ≤ n - 1 are considered. The properties of the functions An,k(x) arising in the inequalities |f(k)(x)|≤An,k (x)││f||W2n[0;1], are studied. The extremum points of An;k are calculated for k = 3, 5 and all admissible n. The global maximum of these functions is found, and the exact embedding constants are calculated.