Resolvent Estimates for the Lamé Operator and Failure of Carleman Estimates

Resolvent Estimates of the Dirac Operator

Global Carleman estimates for waves and applications

Abstract In this article, we extensively develop Carleman estimates for the wave equation and give some applications. We focus on the case of an observation of the flux on a part of the boundary satisfying the Gamma conditions of Lions. We will then consider two applications. The first one deals with the exact controllability problem for the wave equation with potential. Following the duality m...

Carleman Estimates and Absence of Embedded Eigenvalues

Let L = −∆− W be a Schrödinger operator with a potential W ∈ L n+1 2 (R), n ≥ 2. We prove that there is no positive eigenvalue. The main tool is an L − Lp′ Carleman type estimate, which implies that eigenfunctions to positive eigenvalues must be compactly supported. The Carleman estimate builds on delicate dispersive estimates established in [7]. We also consider extensions of the result to var...

Carleman estimates for some elliptic systems

Cohomology with Bounds and Carleman Estimates for the ∂̄-operator on Stein Manifolds

These theorems turned out to be very useful in complex analysis and their applications include the Levi problem with bounds and cohomology with bounds. It is, therefore, natural to seek to generalize these theorems to manifolds. In [5], Theorem 1.1 was so generalized and we generalize Theorem 1.2 in this paper. The term Carleman estimates refers to the estimates in Theorem 1.2 and we use Theore...