Traces and extensions of bounded divergence-measure fields on rough open sets
Traces and extensions of bounded divergence-measure fields on rough open sets
We prove that an open set $\Omega \subset \mathbb{R}^n$ can be approximated by smooth sets of uniformly bounded perimeter from the interior if and only if the open set $\Omega$ satisfies \begin{align*} &\qquad \qquad\qquad\qquad\qquad\qquad\qquad \mathscr{H}^{n-1}(\partial \Omega \setminus \Omega^0)<\infty, \qquad &&\quad\qquad\qquad \qquad\qquad (*) \end{align*} where $\Omega^0$ is the measure-theoretic exterior of …