论文标题
分布正常导数的表示公式
A representation formula for the distributional normal derivative
论文作者
论文摘要
我们证明了$$ \ left \ left \ {\ begin {aligned} - ΔU + v u＆=μ&& \ text {in $ω$，} \\ u＆= 0 && = 0 && pext {on $ \ \partialΩ$，} \ eydect { $$其中$ v \ in l _ {\ mathrm {loc}}^1（ω）$是一个非负函数，$μ$是$ω$的有限鲍勒度量。作为一个应用程序，我们表明，当$ v $是无负的Hopf潜力时，Hopf Lemma几乎在$ \partialΩ上占有任何地方。
We prove an integral representation formula for the distributional normal derivative of solutions of $$ \left\{ \begin{aligned} - Δu + V u &= μ&& \text{in $Ω$,}\\ u &= 0 && \text{on $\partialΩ$,} \end{aligned} \right. $$ where $V \in L_{\mathrm{loc}}^1(Ω)$ is a nonnegative function and $μ$ is a finite Borel measure on $Ω$. As an application, we show that the Hopf lemma holds almost everywhere on $\partialΩ$ when $V$ is a nonnegative Hopf potential.
