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In this paper, we would like to derive three-ball inequalities andpropagation of smallness for the complex second order elliptic equation withdiscontinuous Lipschitz coefficients. As an application of such estimates, westudy the size estimate problem by one pair of Cauchy data on the boundary. Themain ingredient in the derivation of three-ball inequalities and propagation ofsmallness is a local Carleman proved in our recent paper [FVW].

Propagation of smallness and size estimate in the second order elliptic equation with discontinuous complex Lipschitz conductivity