Papers › Boundary determination for hybrid imaging from a single measurement
Boundary determination for hybrid imaging from a single measurement
Tommi Brander, Torbjørn Ringholm
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We recover the conductivity σ at the boundary of a domain from a combination of interior and boundary data, with a single quite arbitrary measurement, in AET or CDII. The argument is elementary and local. More generally, we consider the variable exponent p(·)-Laplacian as a forward model with the interior data σ|∇u|^q, and find out that single measurement specifies the boundary conductivity when p-q ≥1, and otherwise the measurement specifies two alternatives. We present heuristics for selecting between these alternatives. Both p and q may depend on the spatial variable x, but they are assumed to be a priori known. We illustrate the practical situations with numerical examples.
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