Abstract In this paper, we prove the functional Minkowski inequality for ‐torsional rigidity under suitable regularity assumptions, where ‐torsional rigidity can be formulated as the weak solution of an elliptic boundary value problem of the ‐Laplacian. We also establish the Orlicz Brunn–Minkowski and Orlicz Minkowski inequalities for ‐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.
Bu et al. (Mon,) studied this question.