Density problem for Sobolev spaces on Gehring Hayman domains with the ball separation condition in metric measure spaces

Abstract

We prove that for a domain $\Omega$ in a PI space $X$ such that $\Omega$ satisfies the Gehring Hayman condition and the ball separation condition, the Newtonian Sobolev space $N^{1,\infty}(\Omega)$ is dense in the space $N^{1,p}(\Omega)$ for $1 < p < \infty$.