We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on $\partial \Omega \setminus \gamma$. We prove uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.

中文翻译：

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一个逆罗宾谱问题

我们考虑从主特征值和主的正态导数的边界值恢复有界域 $\Omega$ 边界部分 $\gamma\subset\partial\Omega$ 上的 Robin 系数问题具有 Dirichlet 边界条件的拉普拉斯算子在 $\partial \Omega \setminus \gamma$ 上的特征函数。我们证明了逆问题的唯一性以及局部 Lipschitz 稳定性。此外，我们提出了一种具有二维数值计算的迭代重建算法，显示了该方法的准确性。