An inverse problem and an observability inequality for the Lame system with stress boundary condition

摘要

In this article, by a Carleman estimate for solutions of the two-dimensional non-stationary Lame system with the stress boundary condition, we obtain the conditional stability estimate in determining the density and two Lame coefficients which vary spatially by a single observation in a neighbourhood of a suitable subboundary. Moreover, we prove an observability inequality with data measured in the same subdomain.