A density problem for Sobolev spaces on Gromov hyperbolic domains
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. https://doi.org/10.1016/j.na.2016.07.007
Julkaistu sarjassa
Nonlinear Analysis: Theory, Methods and ApplicationsPäivämäärä
2017Tekijänoikeudet
© 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 < ∞.
Julkaisija
Elsevier LtdISSN Hae Julkaisufoorumista
0362-546XAsiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/26176380
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Akatemiatutkija, SA![](/themes/JYX2/images/funders/sa_logo_thumb.jpg)
Lisätietoja rahoituksesta
All authors were partially supported by the Academy of Finland (271983 and 274372).Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Gromov hyperbolicity and quasihyperbolic geodesics
Koskela, Pekka; Lammi, Päivi; Manojlovic, Vesna (Societe Mathematique de France; École normale supérieure, 2014)We characterize Gromov hyperbolicity of the quasihyperbolic metric space (\Omega,k) by geometric properties of the Ahlfors regular length metric measure space (\Omega,d,\mu). The characterizing properties are called the ... -
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 ... -
A Density Result for Homogeneous Sobolev Spaces on Planar Domains
Nandi, Debanjan; Rajala, Tapio; Schultz, Timo (Springer Netherlands, 2019)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). -
Sobolev homeomorphic extensions onto John domains
Koskela, Pekka; Koski, Aleksis; Onninen, Jani (Elsevier Inc., 2020)Given the planar unit disk as the source and a Jordan domain as the target, we study the problem of extending a given boundary homeomorphism as a Sobolev homeomorphism. For general targets, this Sobolev variant of the ... -
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.
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.