In this talk, I consider unique continuation property (UCP) and strong unique continuation property (SUCP) for some anisotropic elastic operator. Our problem is the regularity of Lam\'e parameters with which the UCP holds. In the isotropic case, this problem is considered by Lin-Nakamura-Wang (2010). In this talk we review their results and extend the results to some anisotropic elastic operator which is called the elastic operator with residual tensor. Moreover we also discuss the results of SUCP for this elastic operators

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