ArticleOriginal scientific text
Title
Pointwise inequalities for Sobolev functions and some applications
Authors 1, 2
Affiliations
- Institute of Mathematics, Polish Academy Of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland.
- Institute Of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland.
Abstract
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer's theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Keywords
Sobolev function, Taylor polynomial, approximation, integral representation, Bessel capacity
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