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

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

2008-07-05

arxiv.org/abs/0807.0848v1

Comm. Partial Differential Equations 34, (8) 2009

Mathematics

Analysis of PDEs

16 pages, submitted

Scientific paper

10.1080/03605300903017397

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.

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