  In Acousto-Electric tomography, the objective is to extract information about
the interior electrical conductivity in a physical body from knowledge of the
interior power density data generated from prescribed boundary conditions for
the governing elliptic partial differential equation. In this note, we consider
the problem when the controlled boundary conditions are applied only on a small
subset of the full boundary. We demonstrate using the unique continuation
principle that the Runge approximation property is valid also for this special
case of limited view data. As a consequence, we guarantee the existence of
finitely many boundary conditions such that the corresponding solutions locally
satisfy a non-vanishing gradient condition. This condition is essential for
conductivity reconstruction from power density data. In addition, we adapt an
existing reconstruction method intended for the full data situation to our
setting. We implement the method numerically and investigate the opportunities
and shortcomings when reconstructing from two fixed boundary conditions.
