Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces (Q633098)

The authors consider a parabolic operator \(P=\partial_t-\nabla_x\delta(t,x)\nabla_x\) in \((0,T)\times \Omega\), \(\Omega\) being an open subset of \(\mathbb R^n\), \(n\geq2\), and \(\delta(t,x)\) a piecewise smooth in space yet discontinuous across a smooth interface \(S\). For this operator they prove a global in time, local in space Carleman estimate for \(P\) in the neighborhood of any point of the interface. A global in time and space Carleman estimate on \((0,T)\times M\), \(M\) a manifold, is also derived from the local result.