  We provide answers to some questions raised in a recent work by H. Brezis, J.
Van Schaftingen and Po-Lam Yung concerning the Gagliardo semi-norm
$|u|_{W^{s,q}}$ computed at $s = 1$, when the strong $L^q$ is replaced by weak
$L^q$. In particular, we address generalization of their results for a general
domain and non-smooth functions.
