Strong unique continuation for higher order elliptic equations with Gevrey coefficients

Strong Unique Continuation for Products of Elliptic Operators of Second Order

We study strong unique continuation for products of elliptic operators. The main tools are Carleman inequalities for second order elliptic operators. We obtain strong unique continuation assuming either Gevrey regularity of the coefficients or some pointwise conditions on the coefficients.

Unique Continuation and Complexity of Solutions to Parabolic Partial Differential Equations with Gevrey Coefficients

In this paper, we provide a quantitative estimate of unique continuation (doubling property) for higher-order parabolic partial differential equations with non-analytic Gevrey coefficients. Also, a new upper bound is given on the number of zeros for the solutions with a polynomial dependence on the coefficients.

Carleman Inequalities and the Heat Operator

1. Introduction. The unique continuation property is best understood for second-order elliptic operators. The classic paper by Carleman [8] established the strong unique continuation theorem for second-order elliptic operators that need not have analytic coefficients. The powerful technique he used, the so-called " Carleman weighted inequality, " has played a central role in later developments....

Unique continuation for the elasticity system and a counterexample for second order elliptic systems

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...

Carleman estimates and unique continuation for second order elliptic equations with nonsmooth coefficients