domain-boundary notation

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Domain $\Omega$ in $\mathbb{R}^n$ will have bounday $\partial \Omega$ in $\mathbb{R}^{n-1}$ (Newbie, 2017).
Domain $\Omega$ might have narrow band $\~\Omega$ along Dirichlet boundary (Kang et al., 2021).
Domain $\Omega$ might have difference boundaries $\partial \Omega$, e.g Dirichled $\Gamma_D$, Neumann $\Gamma_N$, and absorbing $\Gamma_A$ (Antonietti et al., 2022).
Domain $\Omega$ might have difference boundaries $\partial \Omega$, e.g Dirichled $\partial\Omega_D$, Neumann $\partial\Omega_N$ (You et al., 2021).