  We study the Possion problem with singular data given by a source supported
on a one dimensional curve strictly contained in a three dimensional domain. We
prove regularity results for the solution on isotropic and on anisotropic
weighted spaces of Kondratiev type. Our technique is based on the study of a
regularized problem. This allows us to exploit the local nature of the
singularity. Our results hold with very few smoothness hypotheses on the domain
and on the support of the data. We also discuss some extensions of our main
results, including the two dimensional case, sources supported on closed curves
and on polygonals.
