Recovering a quasilinear conductivity from boundary measurements

TL;DR

This paper addresses the inverse problem of determining a quasilinear conductivity from boundary measurements, extending previous results to broader classes of conductivities and gradient regimes.

Contribution

It extends the recovery results for isotropic quasilinear conductivities to all real analytic cases and non-analytic cases with growth conditions, including non-homogeneous conductivities.

Findings

Recovery on open subsets of small gradients

Extension to all real analytic conductivities

Recovery under growth assumptions for large gradients

Abstract

We consider the inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.