Carleman Estimates with a Second Large Parameter

Carleman estimates with second large parameter for second order operators

In this paper we prove Carleman type estimates with two large parameters for general linear partial differential operators of second order. By using second large parameter we derive from results for scalar equations first Carleman estimates for dynamical Lamé system with residual stress. We apply these estimates to obtain a Hölder and Lipschitz stability estimates of continuation of solutions o...

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 ...

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

Carleman Estimates and Unique Continuation for Second Order Parabolic Equations with Nonsmooth Coefficients

In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Hölder C 1 3 condition in time. The coefficients in the lower order terms, i.e. the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed ...

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