I am reading "Linear and Nonlinear Functional Analysis with Applications" by Philippe G. Ciarlet and I see the J.L. Lions lemma: Let $\Omega$ be a domain in $\mathbb{R}^N$, then $$ v\in D'(\Omega) \ \ \ \ \text{and} \ \ \ \partial_iv\in H^{-1} $$ implies $v\in L^2(\Omega)$.
When I search this lemma in google, I always find someone say $\Omega$ is an open subset in $\mathbb{R}^N$ with Lipschtiz boundary. I am wondering whether this lemma is related to the boundary?