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In this paper we prove a local Carleman estimate for second order ellipticequations with a general anisotropic Lipschitz coefficients having a jump at aninterface. 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 almostoptimal assumptions on the coefficients and, consequently, the interface.

Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface