标题： $L_q$ Minkowski 问题对于$\mathbf{p}$-调和测度 显示英文标题

标题： The $L_q$ Minkowski problem for $\mathbf{p}$-harmonic measure

摘要： 在本文中，我们考虑与边界值问题解相关的一个极值问题。 我们的主要重点是建立一个与$\mathbf{p}$-调和测度相关的泛函的变分公式，由此得出一种新的测度。 这进一步促使我们研究这种新测度的闵可夫斯基问题。 作为主要结果，我们证明了与$0<q<1$和$1<\mathbf{p}\ne n+1$的$\mathbf{p}$-调和测度相关的$L_q$闵可夫斯基问题解的存在性。 显示英文摘要

摘要： In this paper, we consider an extremal problem associated with the solution to a boundary value problem. Our main focus is on establishing a variational formula for a functional related to the $\mathbf{p}$-harmonic measure, from which a new measure is derived. This further motivates us to study the Minkowski problem for this new measure. As a main result, we prove the existence of solutions to the $L_q$ Minkowski problem associated with the $\mathbf{p}$-harmonic measure for $0<q<1$ and $1<\mathbf{p}\ne n+1$.