Carleman estimates for anisotropic elliptic operators with jumps at an interface
Jérôme Le Rousseau, Nicolás Lerner · Analysis & PDE · 2013
We consider a second-order self-adjoint 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 also prove that the conditions imposed on the weight function are sharp.1. Introduction 1601 2. Framework 1611 3. Estimates for first-order factors 1617 4. Proof of the Carleman estimate 1623 5. Necessity of the geometric assumption on the weight function 1634 Appendix 1637 References 1645The authors wish to thank E. Fernández-Cara for bringing to their attention the importance of Carleman estimates for anisotropic elliptic operators towards applications to biological tissues.Le