In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We make use of
the elementary method so that we are able to impose almost optimal assumptions on the coefficients and, consequently, the interface.
In this paper we prove a quantitative form of the strong unique continuation property for the Lame system when the Lame coefficients $mu$ is Lipschitz and $lambda$ is essentially bounded in dimension $nge 2$. This result is an improvement of our earl
ier result cite{lin5} in which both $mu$ and $lambda$ were assumed to be Lipschitz.
