Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems

Section 4 is devoted to the proof the semi- discrete parabolic Carleman estimate in the case of a discontinuous diffu- sion cofficient for piecewise uniform meshes in

Note however that if the geometry permits the construction of a global continuous weight function ϕ that is smooth except at the interfaces and satisfies the sub-ellipticity

Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic

The Carleman estimate proven in Section 3 allows to give observability estimates that yield null controllability results for classes of semilinear heat equations... We have

The proof for null controllability for the linear parabolic heat equation is then achieved in [11] for the case of a coefficient that exhibits jump of arbitrary sign at an

The Carleman estimate (5) proven in the previous section allows to give observability estimates that yield results of controllability to the trajectories for classes of semilinear

In this paper we prove analoguous results for complex powers of general elliptic operators with analytic coefficients.. Complex powers of elliptic differential

Based on the pseudo-convexity properties we presented above and the pseudo- differential calculus of Section 2, we shall now prove a Carleman estimate with two large