Recovering a quasilinear conductivity from boundary measurements

Ravi Shankar

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arXiv · 1910.07890

Recovering a quasilinear conductivity from boundary measurements

Ravi Shankar

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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.

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Ravi Shankar. 2019-10-12. Recovering a quasilinear conductivity from boundary measurements. https://arxiv.org/abs/1910.07890

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