Unique Continuation for the Elasticity System and a Counterexample for Second-Order Elliptic Systems [chapter]

Carlos Kenig, Jenn-Nan Wang
2016 Harmonic Analysis, Partial Differential Equations, Complex Analysis, Banach Spaces, and Operator Theory (Volume 1)  
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
more » ... 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.
doi:10.1007/978-3-319-30961-3_10 fatcat:eu2aj7terrfvzbzjzagc7i4bua