论文标题
边界响应的非本地逆问题
Nonlocal inverse problem with boundary response
论文作者
论文摘要
本文中感兴趣的问题是研究基于与分数Schrödinger方程相关的边界测量的（非本地）逆问题。令$ 0 <a <1 $，和$ u $ solves \ [\ [case} \ left（（ - δ）^a + q \右） \ end {cases} \]我们表明，通过将边界测量的外部作为$ \ left（u | _ {w}，\ frac {u（x）} {d（x）} {d（x）^a} \ big |_σ\ right）$，可以确定$ q $ q $ q $ q $ q opent $ quop $ subsity，subsity nordecy subsity subsity nordecy copiate copiate ynhor-sep yny-sepatiate ynher-sep yny-和$ d（x）= d（x，\partialΩ）$表示边界距离函数。 我们还讨论了BALL及其应用中大型$ a harmonic功能的本地表征，该功能包括边界独特的延续和局部密度结果。
The problem of interest in this article is to study the (nonlocal) inverse problem of recovering a potential based on the boundary measurement associated with the fractional Schrödinger equation. Let $0<a<1$, and $u$ solves \[\begin{cases} \left((-Δ)^a + q\right)u = 0 \mbox{ in } Ω\\ supp\, u\subseteq \overlineΩ\cup \overline{W}\\ \overline{W} \cap \overlineΩ=\emptyset. \end{cases} \] We show that by making the exterior to boundary measurement as $\left(u|_{W}, \frac{u(x)}{d(x)^a}\big|_Σ\right)$, it is possible to determine $q$ uniquely in $Ω$, where $Σ\subseteq\partialΩ$ be a non-empty open subset and $d(x)=d(x,\partialΩ)$ denotes the boundary distance function. We also discuss local characterization of the large $a$-harmonic functions in ball and its application which includes boundary unique continuation and local density result.
