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This article is cited in 4 scientific papers (total in 4 papers)
Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary
O. V. Matveev Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
In the Sobolev space $W_p^k(\Omega )$, where $\Omega$ is a bounded domain in $\mathbb R^n$ with a Lipschitzian boundary, for an arbitrarily given $m\in \mathbb N$, we construct a basis such that the error of approximation of a function $f\in W_p^k(\Omega )$ the $N$th partial sum of its expansion with respect to this basis can be estimated in terms of the modulus of smoothness $\omega _m(D^kf,N^{-1/n})_{L_p(\Omega )}$ of order $m$.
Received: 26.02.2001
Citation:
O. V. Matveev, “Bases in Sobolev Spaces on Bounded Domains with Lipschitzian Boundary”, Mat. Zametki, 72:3 (2002), 408–417; Math. Notes, 72:3 (2002), 373–382
Linking options:
https://www.mathnet.ru/eng/mzm432https://doi.org/10.4213/mzm432 https://www.mathnet.ru/eng/mzm/v72/i3/p408
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Abstract page: | 479 | Full-text PDF : | 208 | References: | 87 | First page: | 1 |
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