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