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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Unique Continuation for the Elasticity System and a Counterexample for Second-Order Elliptic Systems
verfasst von : Carlos Kenig, Jenn-Nan Wang
Erschienen in: Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)
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Abstract
In this paper we study the global unique continuation property for the elasticity system and the general second-order elliptic system in two dimensions. For the isotropic and the anisotropic systems with measurable coefficients, under certain conditions on coefficients, we show that the global unique continuation property holds. On the other hand, for the anisotropic system, if the coefficients are Lipschitz, we can prove that the global unique continuation is satisfied for a more general class of media. In addition to the positive results, we also present counterexamples to unique continuation and strong unique continuation for general second elliptic systems.