Differentiability points of functions in weighted Sobolev spaces

作者：Tyulenev A I^*

来源：Proceedings of the Steklov Institute of Mathematics, 2013, 283(1): 250-259.

DOI：10.1134/S0081543813080178

We consider weighted Sobolev spaces W (p) (l) , l a a"center dot, 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.

• 出版日期2013-12