Abstract
In this paper, we consider the shape optimization problems for the quantities \lambda(\Omega)T^q(\Omega) , where \Omega varies among open sets of \mathbb{R}^d 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 \lambda(\Omega)T^q(\Omega) , where \Omega varies among open sets of \mathbb{R}^d 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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