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A density problem for Sobolev spaces on Gromov hyperbolic domains

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Koskela, P., Rajala, T., & Zhang, Y. (2017). A density problem for Sobolev spaces on Gromov hyperbolic domains. Nonlinear Analysis: Theory, Methods and Applications, 154, 189-209. doi:10.1016/j.na.2016.07.007
Published in
Nonlinear Analysis: Theory, Methods and Applications
Authors
Koskela, Pekka |
Rajala, Tapio |
Zhang, Yi
Date
2017
Discipline
Matematiikka
Copyright
© 2016 Elsevier Ltd. This is a preprint version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.

 
We prove that for a bounded domain Ω ⊂ Rn which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when Ω is a finitely connected planar domain, the Sobolev space W1, ∞(Ω) is dense in W1, p(Ω) for any 1 ≤ p < ∞. Moreover if Ω is also Jordan or quasiconvex, then C∞(Rn) is dense in W1, p(Ω) for 1 ≤ p < ∞.
Publisher
Elsevier Ltd
ISSN Search the Publication Forum
0362-546X
Keywords
Sobolev space density
DOI
10.1016/j.na.2016.07.007
URI

http://urn.fi/URN:NBN:fi:jyu-201703161669

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