Existence and uniqueness of the solution to the $L_p$ Minkowski problem for the electrostatic $\mathfrak{p}$-capacity are proved when $p \gt 1$ and $1 \lt \mathfrak{p} \lt n$. These results are nonlinear extensions of the very recent solution to the $L_p$ Minkowski problem for $\mathfrak{p}$-capacity when $p = 1$ and $1 \lt \mathfrak{p} \lt n$ by Colesanti et al. and Akman et al., and the classical solution to the Minkowski problem for electrostatic capacity when $p = 1$ and $\mathfrak{p} = 2$ by Jerison.

中文翻译：

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静电$ \ mathfrak {p} $容量的$ L_p $ Minkowski问题

当$ p \ gt 1 $和$ 1 \ lt \ mathfrak {p} \ lt n $时，证明了静电$ \ mathfrak {p} $容量的$ L_p $ Minkowski问题解的存在性和唯一性。这些结果是Colesanti等人在$ p = 1 $和$ 1 \ lt \ mathfrak {p} \ lt n $时，对于$ \ mathfrak {p} $容量的$ L_p $ Minkowski问题的最新解决方案的非线性扩展。。和Akman等。，以及杰里森（Jerison）在$ p = 1 $和$ \ mathfrak {p} = 2 $时静电容量的Minkowski问题的经典解。