Abstract
We consider the Calderón type 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 of Muñoz and Uhlmann 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.
Original language | English (US) |
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Article number | 015014 |
Journal | Inverse Problems |
Volume | 37 |
Issue number | 1 |
DOIs | |
State | Published - Dec 24 2020 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Signal Processing
- Mathematical Physics
- Computer Science Applications
- Applied Mathematics
Keywords
- Calderon problem
- Dirichlet-to-Neumann map
- conductivity
- elliptic
- linearization
- nonlinear
- quasilinear