Carleman estimates with second large parameter for second order operators

Weak Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

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 ...

Carleman estimates for anisotropic elliptic operators with jumps at an interface

We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are sharp.

Control and Cybernetics Generation of Analytic Semi-groups in L 2 for a Class of Second Order Degenerate Elliptic Operators *

Abstract: We study the generation of analytic semigroups in the L topology by second order elliptic operators in divergence form, that may degenerate at the boundary of the space domain. Our results, that hold in two space dimensions, guarantee that the solutions of the corresponding evolution problems support integration by parts. So, this paper provides the basis for deriving Carleman type es...

On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

A. Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are pre...