The Minkowski inequalities for (p,α)$(p,\alpha)$‐torsional rigidity and the extensions on Orlicz spaces

Zhen‐Hui Bu, Meng Qin and Denghui Wu

Mathematische Nachrichten, 2025, vol. 298, issue 9, 3191-3209

Abstract: In this paper, we prove the functional Minkowski inequality for (p,α)$(p,\alpha)$‐torsional rigidity under suitable regularity assumptions, where (p,α)$(p,\alpha)$‐torsional rigidity can be formulated as the weak solution of an elliptic boundary value problem of the p$p$‐Laplacian. We also establish the Orlicz Brunn–Minkowski and Orlicz Minkowski inequalities for (p,α)$(p,\alpha)$‐torsional rigidity, which are extensions of the Brunn–Minkowski and Minkowski inequalities for torsional rigidity. Finally, we describe the equivalence between the Orlicz Brunn–Minkowski inequality and the Orlicz Minkowski inequality.

Date: 2025
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