Resumen de On a reverse Kohler-Jobin inequality
Luca Briani, Giuseppe Buttazzo, Serena Guarino Lo Bianco
In this paper, we consider the shape optimization problems for the quantities λ(Ω)Tq(Ω), where Ω varies among open sets of Rd with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case q>1. We prove that for q large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among nearly spherical domains.In this paper, we consider the shape optimization problems for the quantities λ(Ω)Tq(Ω), where Ω varies among open sets of Rd with a prescribed Lebesgue measure. While the characterization of the infimum is completely clear, the same does not happen for the maximization in the case q>1. We prove that for q large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among nearly spherical domains.
