Existence and uniqueness of the solution to the Lp Minkowski
problem for the electrostatic p-capacity are proved when p > 1
and 1 < p < n. These results are nonlinear extensions of the very
recent solution to the Lp Minkowski problem for p-capacity when
p = 1 and 1 < p < n by Colesanti et al. and Akman et al., and
the classical solution to the Minkowski problem for electrostatic
capacity when p = 1 and p = 2 by Jerison.