  We prove an integral representation formula for the distributional normal
derivative of solutions of $$ \left\{ \begin{aligned} - \Delta u + V u &= \mu
&& \text{in $\Omega$,} u &= 0 && \text{on $\partial\Omega$,} \end{aligned}
\right. $$ where $V \in L_{\mathrm{loc}}^1(\Omega)$ is a nonnegative function
and $\mu$ is a finite Borel measure on $\Omega$. As an application, we show
that the Hopf lemma holds almost everywhere on $\partial\Omega$ when $V$ is a
nonnegative Hopf potential.

Analysis of PDEs