  In this paper, we focus on estimating measure upper bounds of nodal sets of
solutions to the following boundary value problem \begin{equation*} \left\{
\begin{array}{lll} \Delta u+Vu=0\quad \mbox{in}\ \Omega,\\[2mm] u=0\quad
\mbox{on}\ \partial\Omega, \end{array}\right. \end{equation*} where $V\in
W^{1,\infty}(\Omega)$ is a potential and $\Omega\subset \mathbb{R}^n (n\geq2)$
is a bounded domain. We show that upper bounds on the $(n-1)$-dimensional
Hausdorff measure of the nodal sets of $u$ in $\Omega$ is less than or equal to
$$C\Big(1+\log\left(\|\nabla
V\|_{L^{\infty}(\Omega)}+1\right)\Big)\cdot\left(\|V\|_{L^{\infty}(\Omega)}^{\frac{1}{2}}+|\nabla
V\|_{L^{\infty}(\Omega)}^{\frac{1}{2}}+1\right),$$ provided $\partial\Omega$ is
$C^{2}$-smooth and $V$ is analytic. Here $C$ is a positive constant depending
only on $n$ and $\Omega$. In particular, if $\|\nabla V\|_{L^{\infty}(\Omega)}$
is small, the measure upper bound of the of nodal set of $u$ is less than or
equal to $C\left(\|V\|^{\frac{1}{2}}_{L^{\infty}(\Omega)}+1\right)$.
