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.
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