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Properties of extrema of estimates for middle derivatives of odd order in Sobolev classes
- Authors: Garmanova T.A.1, Sheipak I.A.1
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Affiliations:
- Lomonosov Moscow State University
- Issue: Vol 487, No 5 (2019)
- Pages: 487-492
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15871
- DOI: https://doi.org/10.31857/S0869-56524875487-492
- ID: 15871
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Abstract
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.
About the authors
T. A. Garmanova
Lomonosov Moscow State University
Email: iasheip@yandex.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
I. A. Sheipak
Lomonosov Moscow State University
Author for correspondence.
Email: iasheip@yandex.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
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