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arXiv · 2205.09985

The Lp Minkowski problem for q-torsional rigidity

Bin Chen·Xia Zhao·Weidong Wang·Peibiao Zhao
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Abstract

In this paper, we introduce the so-called $L_p$ $q$-torsional measure for $p\in\mathbb{R}$ and $q>1$ by establishing the $L_p$ variational formula for the $q$-torsional rigidity of convex bodies without smoothness conditions. Moreover, we achieve the existence of solutions to the $L_p$ Minkowski problem $w.r.t.$ the $q$-torsional rigidity for discrete measure and general measure when $0 1$.

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Bin Chen, Xia Zhao, Weidong Wang, Peibiao Zhao. 2022-05-20. The Lp Minkowski problem for q-torsional rigidity. https://arxiv.org/abs/2205.09985

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