  The Minkowski problem for electrostatic capacity characterizes measures
generated by electrostatic capacity, which is a well-known variant of the
Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem
for $\mathfrak{p}$-capacity. In particular, the logarithmic case $p=0$ relates
to cone-volumes and therefore has a geometric significance. In this paper we
solve the discrete logarithmic Minkowski problem for $1<\mathfrak{p}<n$ in the
case where the support of the given measure is in general position.
