Lq-Minkowski problem of anisotropic p-torsional rigidity

TL;DR

This paper investigates the $L_q$-Minkowski problem related to anisotropic $p$-torsional rigidity, establishing the existence of solutions under specific conditions for parameters $q$ and $p$, advancing the understanding of geometric analysis.

Contribution

It provides new existence results for the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity for certain ranges of $q$, filling gaps in the mathematical theory.

Findings

Existence of solutions for $0<q<1$

Solutions exist when $1<q eq rac{p}{p-1}+n$

Advances the theory of anisotropic geometric problems

Abstract

In this paper, the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity is considered. The existence of the solution of the $L_q$-Minkowski problem of anisotropic $p$-torsional rigidity with $0<q<1$ and $1<q\neq \frac{p}{p-1}+n$ is given.