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. Takao Ohno, Tetsu Shimomura, Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
  3. Guozhen Lu, Richard Wheeden, High order representation formulas and embedding theorems on stratified groups and generalizations
  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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