The Calderón problem is an inverse source problem

Jan Cristina

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arXiv · 1511.01700

The Calderón problem is an inverse source problem

Jan Cristina

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Abstract

We prove that uniqueness for the Calderón problem on a Riemannian manifold with boundary follows from a hypothetical unique continuation property for the elliptic operator $Δ+V+(Λ^{1}_{t}-q)\otimes (Λ^{2}_{t}-q)$ defined on $\partial\mathcal{M}^{2}\times [0,1]$ where $V$ and $q$ are potentials and $Λ^{i}_{t}$ is a Dirichlet-Neumann operator at depth $t$. This is done by showing that the difference of two Dirichlet-Neumann maps is equal to the Neumann boundary values of the solution to an inhomogeneous equation for said operator, where the source term is a measure supported on the diagonal of $\partial\mathcal{M}^{2}$.

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Jan Cristina. 2015-11-05. The Calderón problem is an inverse source problem. https://arxiv.org/abs/1511.01700

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