We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body when the so-called Dirichlet-to-Neumann map is locally given on a non empty portion of the boundary . We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33:153–171, where the Dirichlet-to-Neumann map was given on all of the boundary. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point. Our arguments also apply when the local Neumann-to-Dirichlet map is available
The local Calderòn problem and the determination at the boundary of the conductivity / Alessandrini, Giovanni; Gaburro, R.. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 34 (8):(2009), pp. 918-936. [10.1080/03605300903017397]
The local Calderòn problem and the determination at the boundary of the conductivity
ALESSANDRINI, GIOVANNI;
2009-01-01
Abstract
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body when the so-called Dirichlet-to-Neumann map is locally given on a non empty portion of the boundary . We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33:153–171, where the Dirichlet-to-Neumann map was given on all of the boundary. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point. Our arguments also apply when the local Neumann-to-Dirichlet map is availablePubblicazioni consigliate
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