let $u$ be a harmonic function in $\omega \subset \mathbb{r}^d.$ it is known that in the interior, the singular set $\mathcal{s}(u) = \{u=|\nabla u|=0 \}$ is $(d-2)$-dimensional, and moreover $\mathcal{s}(u)$ is $(d-2)$-rectifiable and its minkowski content is bounded (depending on the frequency of $u$). we prove the analogue near the boundary for $c^1$-dini domains: if the harmonic function $u$ vanishes on an open subset $e$ of the boundary, then near $e$ the singular set $\mathcal{s}(u) \cap \overline{\omega}$ is $(d-2)$-rectifiable and has bounded minkowski content. dini domain is the optimal domain for which $\nabla$ u is continuous towards the boundary, and in particular every $c^{1,\alpha}$ domain is dini. the main difficulty is the lack of monotonicity formula near the boundary of a dini domain. \\ \\ this is joint work with carlos kenig.