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Optimal three-ball inequalities and quantitative uniqueness for the Lamé system with Lipschitz coefficients. (English) Zbl 1202.35325

Summary: We study the local behavior of a solution to the Lamé system with Lipschitz coefficients in dimension \(n\geq 2\). Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property (SUCP). We solve the open problem of the SUCP for the Lamé system with Lipschitz coefficients in any dimension.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35J56 Boundary value problems for first-order elliptic systems
35B60 Continuation and prolongation of solutions to PDEs
35B45 A priori estimates in context of PDEs
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