Increasing stability in an inverse problem for the acoustic equation

Sei Nagayasu, Gunther Uhlmann, Jenn-Nan Wang

Published 2011-10-24Version 1

In this work we study the inverse boundary value problem of determining the refractive index in the acoustic equation. It is known that this inverse problem is ill-posed. Nonetheless, we show that the ill-posedness decreases when we increase the frequency and the stability estimate changes from logarithmic type for low frequencies to a Lipschitz estimate for large frequencies.