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

TL;DR

This paper establishes existence and uniqueness results for the Lp Minkowski problem related to electrostatic apacity, extending previous solutions to broader parameter ranges and generalizing classical and recent findings.

Contribution

It provides new existence and uniqueness theorems for the Lp Minkowski problem for apacity, covering discrete and general cases for specified parameter ranges.

Findings

Proved solutions for discrete case when p  nd 1<<n.

Established solutions for general case when p  nd 1<nd .

Extended previous results to broader parameter ranges.

Abstract

Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p \geq 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and uniqueness of the solution are given when $p \geq 1$ and $1<\mathfrak{p}\le 2$. These results are non-linear extensions of the very recent solution to the Lp Minkowski problem for $\mathfrak{p}$-capacity when $p=1$ and $1<\mathfrak{p}\le n$ by CNSXYZ, and the classical soution to the Minkowski problem for electrostatic capacity when $p=1$ and $\mathfrak{p}=2$ by Jerison.