In this paper we prove a local Carleman estimate for second order elliptic equations with a general anisotropic Lipschitz coefficients having a jump at an interface. The argument we use is of microlocal nature. Yet, not relying on pseudodifferential calculus, our approach allows one to achieve almost optimal assumptions on the regularity of the coefficients and, consequently, of the interface.
All Science Journal Classification (ASJC) codes
- Applied Mathematics