A note on the Rellich formula in Lipschitz domains

Let $L$ be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain $\Omega$ of $\Bbb R^N$ and having Lipschitz coefficients in $\Omega$. It is shown that the Rellich formula with respect to $\Omega$ and $L$ extends to all functions in the domain $\Cal D=\{u \in H_0^1(\Omega);\, L(u) \in L^2(\Omega)\}$ of $L$. This answers a question of A. Chaïra and G. Lebeau.