利用渐近边界谱数据识别无界电势
Identification of unbounded electric potentials through asymptotic boundary spectral data
摘要：
证明了作用在有界区域$Ω\subset \mathbb{R}^n$中的Dirichlet Laplacian $-Δ+q$的实值电势$q \in L^{\max(2,3 n / 5)}(Ω)$，$n \ge 3$，唯一地由特征值和特征函数的法向导数的边界观测所形成的特征对的渐近性所决定.
英文摘要：
We prove that the real-valued electric potential $q \in L^{\max(2,3 n / 5)}(Ω)$ of the Dirichlet Laplacian $-Δ+q$ acting in a bounded domain $Ω\subset \mathbb{R}^n$, $n \ge 3$, is uniquely determined by the asymptotics of the eigenpairs formed by the eigenvalues and the boundary observation of the normal derivative of the eigenfunctions.
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