arXiv subjects

Yi Ru-Ya Zhang

Publications and source records attributed to Yi Ru-Ya Zhang.

38 records · Page 3Linked to original sources

arXiv2016

A density problem for Sobolev spaces on Gromov hyperbolic domains

We prove that for a bounded domain $Ω\subset \mathbb R^n$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $Ω$ is a finitely connected planar domain, the Sobolev space $W^{1,\,\infty}(Ω)$ is dense in $W^{1,\,p}(Ω)$ for any $1\le p<\infty$. Moreover if $Ω$ is also Jordan or quasiconvex, then $C^{\infty}(\mathbb R^n)$ is dense in $W^{1,\,p}(Ω)$ for $1\le p<\infty$.

math.FA↗

arXiv2015

A density problem for Sobolev spaces on planar domains

We prove that for a bounded simply connected domain $Ω\subset \mathbb R^2$, the Sobolev space $W^{1,\,\infty}(Ω)$ is dense in $W^{1,\,p}(Ω)$ for any $1\le p<\infty$. Moreover, we show that if $Ω$ is Jordan, then $C^{\infty}(\mathbb R^2)$ is dense in $W^{1,\,p}(Ω)$ for $1\le p<\infty$.

math.CA↗