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;

D O I：

暂无

中图分类号：

学科分类号：

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.

引用

页码：250 / 259

页数：9

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