Inverse source problem with regularity constraints: normal solution and nonradiating source components

The use of regularity constraints in formulating the scalar inverse source problem (ISP) is investigated. Two kinds of regularity constraints are considered: compact supportness in a given source region, and normal differentiability on the boundary of that region. Normal solutions (minimum L 2 norm solutions) to the ISP for square-integrable ( L 2 ) scalar sources with and without the above-mentioned regularity constraints are derived and compared. The (generally nontrivial) nonradiating parts of the corresponding normal solutions are evaluated.