  We recover the conductivity $\sigma$ 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 $p(\cdot)$-Laplacian as a forward
model with the interior data $\sigma |\nabla u|^q$, and find out that single
measurement specifies the boundary conductivity when $p-q \ge 1$, 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.
