Convex Solutions to the Virtual Source Reflector Problem

We greatly expand upon the results of Kochengin, Oliker and Tempeski [S. Kochengin, V. Oliker, O. von Tempeski, On the design of reflectors with prescribed distribution of virtual sources and intensities, Inverse Problems 14 (1998) 661-678.] to include results for uniqueness in the general case. We also include results for existence in the rotationally symmetric case and the case where the target set is sufficiently small.