Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface

Abstract

In this paper we prove a Hölder propagation of smallness for solutions to second order parabolic equations whose general anisotropic leading coefficient has a jump at an interface. We assume that the leading coefficient is Lipschitz continuous with respect to the parabolic distance on both sides of the interface. The main effort consists in proving a local Carleman estimate for this parabolic operator.