On Stability for an Inverse Hyperbolic Problem

KiHyun Yun
Michigan State University
kyun@math.msu.edu

Abstract: In this talk, we focus on the inverse problem of determining the potential by the Neumann to Dirichlet map in the wave equation in with . Here, we establish a Hölder type stability with exponent as follows: for any small , there exists such that

when for some . Here, represents the operator norm.

To mention the previous related work, twenty years ago (1988), using Sylvester and Uhlmann s method that is well known in inverse problems, Ziqi Sun, and Alessandrini and Sylvester obtained Holder stability

There has been no remarkable improvement in this result, even though Yamamoto made some results under the strong condition.

As it mentioned in the abstract, we have obtained a nearly Lipschitz type stability estimate under the same condition as Sun.