  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.
