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• W2899198670 abstract "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 qquadqquadqquadqquadqquadqquad mathscr{H}^{n-1}(partial Omega setminus Omega^0)<infty, qquad &&quadqquadqquad qquadqquad (*) end{align*} where $Omega^0$ is the measure-theoretic exterior of $Omega$. Furthermore, we show that condition (*) implies that the open set $Omega$ is an extension domain for bounded divergence-measure fields, which improves the previous results that require a strong condition that $mathscr{H}^{n-1}(partial Omega)<infty$. As an application, we establish a Gauss-Green formula up to the boundary on any open set $Omega$ satisfying condition (*) for bounded divergence-measure fields, for which the corresponding normal trace is shown to be a bounded function concentrated on $partial Omega setminus Omega^0$. This new formula does not require the set of integration to be compactly contained in the domain where the vector field is defined. In addition, we also analyze the solvability of the divergence equation on a rough domain with prescribed trace on the boundary, as well as the extension domains for bounded $BV$ functions." @default.
• W2899198670 created "2018-11-09" @default.
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• W2899198670 date "2018-10-30" @default.
• W2899198670 modified "2023-09-27" @default.
• W2899198670 title "Traces and Extensions of Bounded Divergence-Measure Fields on Rough Open Sets" @default.
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• W2899198670 hasPublicationYear "2018" @default.
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