Jacobian of solutions to the conductivity equation in limited view

The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction electrical conductivity in a domain that can only be accessed from its exterior. In inversion procedure, solutions to equation play central role. particular, it important Jacobian non-vanishing. present paper we address two-dimensional limited view setting, where part boundary controlled by non-zero Dirichlet condition, while on remaining there zero condition. For this propose sufficient conditions functions so corresponding regard allow for discontinuous functions, which requires use weighted Sobolev spaces. We implement procedure reconstructing power density data numerically and investigate how setting affects quality reconstructions.