论文标题
一类空心球中的稳定性估计值
Stability estimates for an inverse Steklov problem in a class of hollow spheres
论文作者
论文摘要
在本文中，我们研究了具有空心球体拓扑并配备扭曲的产品指标的一类N维歧管中的反向steklov问题。确切地说，我们旨在研究扭曲功能的持续依赖性，以否认扭曲产品相对于Steklov Spectrum。我们首先表明，直到指数降低误差的知识足以确定边界附近的翘曲函数。其次，当翘曲功能相对于1/2对称时，我们证明了反向steklov问题中的对数型稳定性估计值。作为最后的结果，我们证明了相应的calder {ó} n问题的对数型稳定性估计。
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 dening the warped product with respect to the Steklov 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 Calder{ó}n problem.
