A density problem for Sobolev spaces on Gromov hyperbolic domains
| Autor: | Yi Ru-Ya Zhang, Tapio Rajala, Pekka Koskela |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
density Applied Mathematics 010102 general mathematics ta111 Sobolev space 01 natural sciences Domain (mathematical analysis) Functional Analysis (math.FA) Mathematics - Functional Analysis Quasiconvex function Planar tiheys Bounded function 0103 physical sciences Metric (mathematics) FOS: Mathematics Mathematics::Metric Geometry 010307 mathematical physics 0101 mathematics Analysis Mathematics |
| Popis: | We prove that for a bounded domain $\Omega\subset \mathbb R^n$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $\Omega$ is a finitely connected planar domain, the Sobolev space $W^{1,\,\infty}(\Omega)$ is dense in $W^{1,\,p}(\Omega)$ for any $1\le p Comment: 22 pages, 6 figures |
| Databáze: | OpenAIRE |
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