Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Denghui Wu

College of Science, Northwest A&F University, Yangling, Shaanxi, China

wudenghui66@163.com

Zhen-Hui Bu

College of Science, Northwest A&F University, Yangling, Shaanxi, China

buzhenhui14@163.com

Keywords

  • Stability
  • Brunn-Minkowski inequality
  • Borell-Brascamp-Lieb inequality
  • p-torsional rigidity
  • p-Laplace operator

Mathematics Subject Classification

35J60, 39B62, 52A20, 47J05, 26A51

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Suggested citation

D. Wu, M. Qin, Z.-H. Bu. “Quantitative Stability of Brunn-Minkowski Inequalities for the p-Torsional Rigidity.” Journal of Convex Analysis 33 (2026), No. 1&2, 473–495. https://doi.org/10.68381/jca33030

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