Hu, J. (2025). The Lₚ-Brunn–Minkowski inequalities for variational functionals with 0 ≤ p < 1. Calculus of Variations and Partial Differential Equations, 64(8), Article 241. https://doi.org/10.1007/s00526-025-03090-7
The infinitesimal forms of the Lₚ-Brunn–Minkowski inequalities for variational functionals, such as the q-capacity, the torsional rigidity, and the first eigenvalue of the Laplace operator, are investigated for p≥0. These formulations yield Poincaré-type inequalities related to these functionals. As an application, the Lₚ-Brunn–Minkowski inequalities for torsional rigidity with 0≤p<1 are confirmed for small smooth perturbations of the unit ball.
