Carleman-type estimates and the Neumann problem

the investigation of the relationship between type a and type b personalities and quality of translation

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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

On Carleman estimates with two large parameters

A Carleman estimate for a differential operator P is a weighted energy estimate with a weight of exponential form exp(τφ) that involves a large parameter, τ > 0. The function φ and the operator P need to fulfill some sub-ellipticity properties that can be achieved for instance by choosing φ = exp(αψ), involving a second large parameter, α > 0, with ψ satisfying some geometrical conditions. The ...