$\|u\|_{L^{2}(\Omega)} \leqslant C \|Du\| _{L^{2}(\Omega)} + \|u\| _{L^2{(\partial{\Omega})}}$ for $u\in H^{1}=W^{1,2}(\Omega)$
(Sobolev space with one weak derivative integrable in square), where $\Omega = \{ x\in\mathbb{R}^{n}:\ 1<|x|<2 \}$?
(we do not assume, that the trace of $u$ vanishes).