Characterizations of Sobolev functions that vanish on a part of the boundary
M Egert, P Tolksdorf - arXiv preprint arXiv:1609.05749, 2016 - arxiv.org
arXiv preprint arXiv:1609.05749, 2016•arxiv.org
Let $\Omega $ be a bounded domain in R n with a Sobolev extension property around the
complement of a closed part D of its boundary. We prove that a function u $\in $ W 1, p
($\Omega $) vanishes on D in the sense of an interior trace if and only if it can be
approximated within W 1, p ($\Omega $) by smooth functions with support away from D. We
also review several other equivalent characterizations, so to draw a rather complete picture
of these Sobolev functions vanishing on a part of the boundary.
complement of a closed part D of its boundary. We prove that a function u $\in $ W 1, p
($\Omega $) vanishes on D in the sense of an interior trace if and only if it can be
approximated within W 1, p ($\Omega $) by smooth functions with support away from D. We
also review several other equivalent characterizations, so to draw a rather complete picture
of these Sobolev functions vanishing on a part of the boundary.
Let be a bounded domain in R n with a Sobolev extension property around the complement of a closed part D of its boundary. We prove that a function u W 1,p () vanishes on D in the sense of an interior trace if and only if it can be approximated within W 1,p () by smooth functions with support away from D. We also review several other equivalent characterizations, so to draw a rather complete picture of these Sobolev functions vanishing on a part of the boundary.
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