Differentiability points of functions in weighted Sobolev spaces

被引：0
|
作者：
A. I. Tyulenev
机构：
[1] Moscow Institute of Physics and Technology (State University),
来源：
Proceedings of the Steklov Institute of Mathematics | 2013年 / 283卷
关键词：
Sobolev Space; STEKLOV Institute; Weighted Sobolev Space; Minkowski Inequality; Taylor Formula;
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摘要：
We consider weighted Sobolev spaces Wpl, l ∈ ℕ, with weighted Lp-norm of higher derivatives on an n-dimensional cube-type domain. The weight γ depends on the distance to an (n − d)-dimensional face E of the cube. We establish the property of uniform Lp-differentiability of functions in these spaces on the face E of an appropriate dimension. This property consists in the possibility of Lp-approximation of the values of a function near E by a polynomial of degree l − 1.
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页码：250 / 259
页数：9
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