Does exists a short, simple proof of the inequality

$ \|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).