Remarks on the anisotropic Calderón problem

Abstract

We show uniqueness results for the anisotropic Calderón problem stated on transversally anisotropic manifolds. Moreover, we give a convexity result for the range of Dirichlet-to-Neumann maps on general Riemannian manifolds near the zero potential. Finally, we present results for Calderón type inverse problems associated to semilinear elliptic equations on general Riemannian manifolds.

References in corpus (6)

• Limiting Carleman weights and anisotropic inverse problems
• The Poisson embedding approach to the Calderón problem
• An inverse problem for a semi-linear elliptic equation in Riemannian geometries
• The linearized Calderon problem in transversally anisotropic geometries
• Boundary and lens rigidity for non-convex manifolds
• Reconstruction in the Calderón problem on conformally transversally anisotropic manifolds

Cited by in corpus (2)

• Rigidity of inverse problems for nonlinear elliptic equations on manifolds
• Increasing stability of the first order linearized inverse Schrödinger potential problem with integer power type nonlinearities