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Trudy Mat. Inst. Steklova, 2013, Volume 283, Pages 257–266 (Mi tm3501)  

Differentiability points of functions in weighted Sobolev spaces

A. I. Tyulenev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia

Abstract: We consider weighted Sobolev spaces $W_p^l$, $l\in\mathbb N$, with weighted $L_p$-norm of higher derivatives on an $n$-dimensional cube-type domain. The weight $\gamma$ depends on the distance to an $(n-d)$-dimensional face $E$ of the cube. We establish the property of uniform $L_p$-differentiability of functions in these spaces on the face $E$ of an appropriate dimension. This property consists in the possibility of $L_p$-approximation of the values of a function near $E$ by a polynomial of degree $l-1$.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00744
10-01-91331
Ministry of Education and Science of the Russian Federation 2.1.1/1662
This work was supported by the Russian Foundation for Basic Research (project nos. 11-01-00744 and 10-01-91331) and by the Ministry of Education and Science of the Russian Federation (project no. 2.1.1/1662).


DOI: https://doi.org/10.1134/S0371968513040171

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 283, 250–259

Bibliographic databases:

UDC: 517.518.23
Received in February 2013

Citation: A. I. Tyulenev, “Differentiability points of functions in weighted Sobolev spaces”, Function theory and equations of mathematical physics, Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth, Trudy Mat. Inst. Steklova, 283, MAIK Nauka/Interperiodica, Moscow, 2013, 257–266; Proc. Steklov Inst. Math., 283 (2013), 250–259

Citation in format AMSBIB
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\by A.~I.~Tyulenev
\paper Differentiability points of functions in weighted Sobolev spaces
\inbook Function theory and equations of mathematical physics
\bookinfo Collected papers. In commemoration of the 90th anniversary of Lev Dmitrievich Kudryavtsev's birth
\serial Trudy Mat. Inst. Steklova
\yr 2013
\vol 283
\pages 257--266
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968513040171}
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\jour Proc. Steklov Inst. Math.
\yr 2013
\vol 283
\pages 250--259
\crossref{https://doi.org/10.1134/S0081543813080178}
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