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arXiv · 0807.0848

The local Calderon problem and the determination at the boundary of the conductivity

Giovanni Alessandrini·Romina Gaburro
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Abstract

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $Ω\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $Γ$ of the boundary $\partialΩ$. We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33 (2001), no. 1, 153--171, where the Dirichlet-to-Neumann map was given on all of $\partialΩ$ instead. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point $y\inΓ$. Our arguments also apply when the local Neumann-to-Dirichlet map is available.

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Giovanni Alessandrini, Romina Gaburro. 2008-07-05. The local Calderon problem and the determination at the boundary of the conductivity. https://doi.org/10.1080/03605300903017397

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