The two-dimensional inverse conductivity problem. (English) Zbl 1439.32029
Summary: In this article, we introduce a process to reconstruct a Riemann surface with boundary equipped with a linked conductivity tensor from its boundary and the Dirichlet-Neumann operator associated with this conductivity. When initial data come from a two-dimensional real Riemannian surface equipped with a conductivity tensor, this process recovers its conductivity structure.
MSC:
| 32F99 | Geometric convexity in several complex variables |
| 32D15 | Continuation of analytic objects in several complex variables |
| 32V15 | CR manifolds as boundaries of domains |
| 35R30 | Inverse problems for PDEs |
| 58J32 | Boundary value problems on manifolds |
Keywords:
Riemann surface; Dirichlet-to-Neumann problem; Green function; conductivity; shock wave; embeddingReferences:
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