Carleman estimate for complex second order elliptic operators with discontinuous Lipschitz coefficients

Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface

In this paper we prove a Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. Our approach does not rely on the techniques of microlocal analysis. We make use of the elementary method so that we are able to impose almost optimal assumptions on the coefficients and, consequently, the interface. It is possible that ...

Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate

In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work [5]. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.

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...

The Regularity Problem for Second Order Elliptic Operators with Complex-valued Bounded Measurable Coefficients

The present paper establishes a certain duality between the Dirichlet and Regularity problems for elliptic operators with t-independent complex bounded measurable coefficients (t being the transversal direction to the boundary). To be precise, we show that the Dirichlet boundary value problem is solvable in Lp ′ , subject to the square function and non-tangential maximal function estimates, if ...

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