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

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