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

Abstract

We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega \subset {\mathbb{R}}^n$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary $\partial \Omega$. 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 $\partial \Omega$ instead. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point $y\in \Gamma$. Our arguments also apply when the local Neumann-to-Dirichlet map is available.

arXiv comment16 pages, submitted

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