Size of the zero set of solutions of elliptic PDEs near the boundary of Lipschitz domains with small Lipschitz constant

Let $\Omega \subset \mathbb R^d$ be a $C^1$ domain or, more generally, Lipschitz with small constant and $A(x)$ $d \times d$ uniformly elliptic, symmetric matrix coefficients. Assume $u$ is harmonic in $\Omega$, or greater generality solves $\operatorname{div}(A(x)\nabla u)=0$ vanishes on $\Sigma = \partial\Omega \cap B$ for some ball $B$. We study the dimension of singular set $\Sigma$, particular we show that there countable family open balls $(B_i)_i$ such $u|_{B_i \Omega}$ does not change sign $K \backslash \bigcup_i B_i$ has Minkowski smaller than $d-1-\epsilon$ any compact \Sigma$. also find upper bounds $(d-1)$-dimensional Hausdorff measure zero intersecting $\Sigma$ terms frequency. As consequence, prove new unique continuation principle at boundary this class functions order vanishing all points bounded except most $d-1-\epsilon$.