Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions
Jérôme Rousseau, Nicolás Lerner · Journées Équations aux dérivées partielles · 2010
We consider a second-order selfadjoint elliptic operator with an anisotropic diffusion matrix having a jump across a smooth hypersurface. We prove the existence of a weight-function such that a Carleman estimate holds true. We moreover prove that the conditions imposed on the weight function are necessary.