  We consider the problem of finding a measure from the given values of its
logarithmic potential on the support. It is well known that a solution to this
problem is given by the generalized Laplacian. The case of our main interest is
when the support is contained in a rectifiable curve, and the measure is
absolutely continuous with respect to the arclength on this curve. Then the
generalized Laplacian is expressed by a sum of normal derivatives of the
potential. Such representation was available for smooth curves, and we show it
holds for any rectifiable curve in the plane. We also relax the assumptions
imposed on the potential.
  Finding a measure from its potential often leads to another closely related
problem of solving a singular integral equation with Cauchy kernel. The theory
of such equations is well developed for smooth curves. We generalize this
theory to the class of Ahlfors regular curves and arcs, and characterize the
bounded solutions on arcs.
