Definitions of Sobolev classes on metric spaces

Bruno Franchi; Piotr Hajłasz; Pekka Koskela

Annales de l'institut Fourier (1999)

  • Volume: 49, Issue: 6, page 1903-1924
  • ISSN: 0373-0956

Abstract

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There have been recent attempts to develop the theory of Sobolev spaces W 1 , p on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case p = 1 .

How to cite

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Franchi, Bruno, Hajłasz, Piotr, and Koskela, Pekka. "Definitions of Sobolev classes on metric spaces." Annales de l'institut Fourier 49.6 (1999): 1903-1924. <http://eudml.org/doc/75406>.

@article{Franchi1999,
abstract = {There have been recent attempts to develop the theory of Sobolev spaces $W^\{1,p\}$ on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case $p=1$.},
author = {Franchi, Bruno, Hajłasz, Piotr, Koskela, Pekka},
journal = {Annales de l'institut Fourier},
keywords = {Sobolev spaces; metric spaces; doubling measures; Carnot-Carathéodory spaces; Hörmander’s rank condition; Poincaré inequality; doubling condition},
language = {eng},
number = {6},
pages = {1903-1924},
publisher = {Association des Annales de l'Institut Fourier},
title = {Definitions of Sobolev classes on metric spaces},
url = {http://eudml.org/doc/75406},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Franchi, Bruno
AU - Hajłasz, Piotr
AU - Koskela, Pekka
TI - Definitions of Sobolev classes on metric spaces
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 6
SP - 1903
EP - 1924
AB - There have been recent attempts to develop the theory of Sobolev spaces $W^{1,p}$ on metric spaces that do not admit any differentiable structure. We prove that certain definitions are equivalent. We also define the spaces in the limiting case $p=1$.
LA - eng
KW - Sobolev spaces; metric spaces; doubling measures; Carnot-Carathéodory spaces; Hörmander’s rank condition; Poincaré inequality; doubling condition
UR - http://eudml.org/doc/75406
ER -

References

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