# Existence of triangulation of Lipschitz domains

Consider a bounded Lipschitz domain $\Omega \subset \mathbb R^n$.

Q1: Can its closure $\overline\Omega$ be triangulated?

Q2: If yes, can the triangulation be chosen as finite? Furthermore, how regular can the triangulation be? For example, an optimal result would be a finite triangulation consisting of topological simplices which share at most one face with the boundary, and whose faces are flat with the possible exception of the boundary face.