  Given an open set with finite perimeter $\Omega\subset \mathbb{R}^n$, we
consider the space $LD_\gamma^{p}(\Omega)$, $1\leq p<\infty$, of functions with
$p$th-integrable deformation tensor on $\Omega$ and with $p$ th-integrable
trace value on the essential boundary of $\Omega$. We establish the continuous
embedding $LD_\gamma^{p}(\Omega)\subset L^{pN/(N-1)}(\Omega)$. The space
$LD_\gamma^{p}(\Omega)$ and this embedding arise naturally in studying the
motion of rigid bodies in a viscous, incompressible fluid.
