Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces

Takao Ohno; Tetsu Shimomura

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 2, page 371-394
  • ISSN: 0011-4642

Abstract

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We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.

How to cite

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Ohno, Takao, and Shimomura, Tetsu. "Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces." Czechoslovak Mathematical Journal 66.2 (2016): 371-394. <http://eudml.org/doc/280087>.

@article{Ohno2016,
abstract = {We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.},
author = {Ohno, Takao, Shimomura, Tetsu},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sobolev space; metric measure space; Hajłasz-Sobolev space; Musielak-Orlicz space; capacity; variable exponent; zero boundary values; Riesz potential; Sobolev inequality; variable exponent; metric measure space; nondoubling measure},
language = {eng},
number = {2},
pages = {371-394},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces},
url = {http://eudml.org/doc/280087},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Ohno, Takao
AU - Shimomura, Tetsu
TI - Musielak-Orlicz-Sobolev spaces with zero boundary values on metric measure spaces
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 371
EP - 394
AB - We define and study Musielak-Orlicz-Sobolev spaces with zero boundary values on any metric space endowed with a Borel regular measure. We extend many classical results, including completeness, lattice properties and removable sets, to Musielak-Orlicz-Sobolev spaces on metric measure spaces. We give sufficient conditions which guarantee that a Sobolev function can be approximated by Lipschitz continuous functions vanishing outside an open set. These conditions are based on Hardy type inequalities.
LA - eng
KW - Sobolev space; metric measure space; Hajłasz-Sobolev space; Musielak-Orlicz space; capacity; variable exponent; zero boundary values; Riesz potential; Sobolev inequality; variable exponent; metric measure space; nondoubling measure
UR - http://eudml.org/doc/280087
ER -

References

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