Carleman estimates for elliptic operators with jumps at an interface: Anisotropic case and sharp geometric conditions

Abstract

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.

43 pages

Cited by in corpus (4)

• Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface
• Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems
• Carleman estimate for second order elliptic equations with Lipschitz leading coefficients and jumps at an interface
• Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate