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

Abstract

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 by M. Bellassoued and J. Le Rousseau (2018) and the arguments by 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.