A Density Result for Homogeneous Sobolev Spaces on Planar Domains
Nandi, D., Rajala, T., & Schultz, T. (2019). A Density Result for Homogeneous Sobolev Spaces on Planar Domains. Potential Analysis, 51(4), 483-498. https://doi.org/10.1007/s11118-018-9720-8
Published in
Potential AnalysisDate
2019Copyright
© Springer Nature B.V. 2018
We show that in a bounded simply connected planar domain Ω the smooth Sobolev functions Wk,∞(Ω) ∩ C∞(Ω) are dense in the homogeneous Sobolev spaces Lk,p(Ω).
Publisher
Springer NetherlandsISSN Search the Publication Forum
0926-2601Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/28197176
Metadata
Show full item recordCollections
Additional information about funding
All authors partially supported by the Academy of Finland.License
Related items
Showing items with similar title or keywords.
-
Planar Sobolev extension domains
Zhang, Yi (University of Jyväskylä, 2017)This doctoral thesis deals with geometric characterizations of bounded planar simply connected Sobolev extension domains. It consists of three papers. In the first and third papers we give full geometric characterizations ... -
Bi-Lipschitz invariance of planar BV- and W1,1-extension domains
García-Bravo, Miguel; Rajala, Tapio; Zhu, Zheng (American Mathematical Society (AMS), 2022) -
Dimension estimates for the boundary of planar Sobolev extension domains
Lučić, Danka; Rajala, Tapio; Takanen, Jyrki (Walter de Gruyter GmbH, 2023)We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev W1,pW1,p -extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is ... -
A density result on Orlicz-Sobolev spaces in the plane
Ortiz, Walter A.; Rajala, Tapio (Elsevier, 2021)We show the density of smooth Sobolev functions Wk,∞(Ω)∩C∞(Ω) in the Orlicz-Sobolev spaces Lk,Ψ(Ω) for bounded simply connected planar domains Ω and doubling Young functions Ψ. -
A density problem for Sobolev spaces on Gromov hyperbolic domains
Koskela, Pekka; Rajala, Tapio; Zhang, Yi (Elsevier Ltd, 2017)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) ...