Calculus of Variations and Geometric Measure Theory

B. Chen - X. Zhao - W. Wang - P. Zhao

The Lp Minkowski problem for q-torsional rigidity

created by zhao on 24 Oct 2022

[BibTeX]

Accepted paper

Inserted: 24 oct 2022

Journal: Advances in Calculus of Variations
Year: 2022
Doi: 10.1515/acv-2022-0041

ArXiv: 2205.09985 PDF

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 measures and general measures when $0<p<1$ and $q>1$.