Journal of Convex Analysis 33 (2026), No. 1&2, 473--495
Copyright Heldermann Verlag 2026
Quantitative Stability of Brunn-Minkowski Inequalities for the p-Torsional Rigidity
Denghui Wu
College of Science, Northwest A&F University, Yangling, Shaanxi, China
wudenghui66@163.com
Meng Qin
College of Science, Northwest A&F University, Yangling, Shaanxi, China
qm1272098212@163.com
Zhen-Hui Bu
College of Science, Northwest A&F University, Yangling, Shaanxi, China
buzhenhui14@163.com
We establish the quantitative Brunn-Minkowski inequality and the quantitative Urysohn inequality for p-torsional rigidity. Here the p-torsional rigidity can be formulated by the weak solution of the boundary value problem of p-Laplace equation. In order to prove the main results, we establish the relation between the Borell-Brascamp-Lieb deficit and the Brunn-Minkowski deficit, and then use the relation to prove two different stability of the Borell-Brascamp-Lieb inequality for p-concave functions with p > 0. The constants in our stability results are independent on the parameter p and the integrals of given functions, and thus also improve the results given by Ghilli and Salani about the case p = 2.
Keywords: Stability, Brunn-Minkowski inequality, Borell-Brascamp-Lieb inequality, p-torsional rigidity, p-Laplace operator.
MSC: 35J60, 39B62, 52A20, 47J05, 26A51.
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