Pointwise inequalities for Sobolev functions and some applications

Bogdan Bojarski; Piotr Hajłasz

Studia Mathematica (1993)

  • Volume: 106, Issue: 1, page 77-92
  • ISSN: 0039-3223

Abstract

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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 C m functions both in norm and capacity.

How to cite

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Bojarski, Bogdan, and Hajłasz, Piotr. "Pointwise inequalities for Sobolev functions and some applications." Studia Mathematica 106.1 (1993): 77-92. <http://eudml.org/doc/216004>.

@article{Bojarski1993,
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 $C^m$ functions both in norm and capacity.},
author = {Bojarski, Bogdan, Hajłasz, Piotr},
journal = {Studia Mathematica},
keywords = {Sobolev function; Taylor polynomial; approximation; integral representation; Bessel capacity; pointwise inequalities for Sobolev functions; Michael-Ziemer's theorem},
language = {eng},
number = {1},
pages = {77-92},
title = {Pointwise inequalities for Sobolev functions and some applications},
url = {http://eudml.org/doc/216004},
volume = {106},
year = {1993},
}

TY - JOUR
AU - Bojarski, Bogdan
AU - Hajłasz, Piotr
TI - Pointwise inequalities for Sobolev functions and some applications
JO - Studia Mathematica
PY - 1993
VL - 106
IS - 1
SP - 77
EP - 92
AB - 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 $C^m$ functions both in norm and capacity.
LA - eng
KW - Sobolev function; Taylor polynomial; approximation; integral representation; Bessel capacity; pointwise inequalities for Sobolev functions; Michael-Ziemer's theorem
UR - http://eudml.org/doc/216004
ER -

References

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  21. [MZ] J. Michael and W. Ziemer, A Lusin type approximation of Sobolev functions by smooth functions, in: Contemp. Math. 42, Amer. Math. Soc., 1985, 135-167. 
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  26. [Z2] W. Ziemer, Weakly Differentiable Functions, Springer, 1989. 

Citations in EuDML Documents

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  1. Agnieszka Kałamajska, On lower semicontinuity of multiple integrals
  2. Guozhen Lu, Richard Wheeden, High order representation formulas and embedding theorems on stratified groups and generalizations
  3. Takao Ohno, Tetsu Shimomura, Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
  4. Takao Ohno, Tetsu Shimomura, Musielak-Orlicz-Sobolev spaces on metric measure spaces
  5. Irene Fonseca, Nicola Fusco, Paolo Marcellini, Topological degree, Jacobian determinants and relaxation

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