Lp Minkowski problem for electrostatic $\mathfrak{p}$-capacity

Abstract

Existence and uniqueness of the solution to the discrete L p Minkowski problem for p-capacity are proved when p ≥ 1 and 1 < p < n. For general L p Minkowski problem for p-capacity, existence and uniqueness of the solution are given when p ≥ 1 and 1 < p ≤ 2. These results are non-linear extensions of the very recent solution to the L p Minkowski problem for p-capacity when p = 1 and 1 < p < n by CNSXYZ, and the classical solution to the Minkowski problem for electrostatic capacity when p = 1 and p = 2 by Jerison.