Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients

In this paper, we derive a local Carleman estimate for the complex second order elliptic operator with Lipschitz coefficients having jump discontinuities. Combing the result in [M. Bellassoued, J. Le Rousseau 2018] and the arguments in [M. Di Cristo, E. Francini, C.-L. Lin, S. Vessella, and J.-N. Wang, 2017], we present an elementary method to derive the Carleman estimate under the optimal regularity assumption on the coefficients.