In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the warping function defining the warped product with respect to theSteklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, when the warping functions are symmetric with respect to 1/2, we prove a log-type stability estimate in the inverse Steklov problem. As a last result, we prove a log-type stability estimate for the corresponding Calderón problem.

中文翻译：

---

一类空心球中逆Steklov问题的稳定性估计

在本文中，我们研究了一类具有空心球拓扑并配备了翘曲乘积度量的n维流形中的逆Steklov问题。精确地，我们旨在研究变形函数相对于Steklov光谱的连续依赖性。我们首先表明，直到指数递减误差为止的Steklov谱的知识足以唯一确定边界附近的翘曲函数。其次，当翘曲函数关于1/2对称时，我们证明了逆Steklov问题中的对数型稳定性估计。作为最后的结果，我们证明了对应的Calderón问题的对数型稳定性估计。