The Calderón inverse problem for isotropic quasilinear conductivities

Abstract

We prove a global uniqueness result for the Calderón inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension $n\ge 3$. Performing higher order linearizations of the nonlinear Dirichlet--to--Neumann map, we reduce the problem of the recovery of the differentials of the quasilinear conductivity, which are symmetric tensors, to a completeness property for certain anisotropic products of solutions to the linearized equation. The completeness property is established using complex geometric optics solutions to the linearized conductivity equation, whose amplitudes concentrate near suitable two dimensional planes.

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Cited by in corpus (1)

• An inverse boundary value problem for the inhomogeneous porous medium equation