论文标题
在反向Kohler-Jobin不平等上
On a reverse Kohler-Jobin inequality
论文作者
论文摘要
我们考虑数量$λ（ω）t^q（ω）$的形状优化问题，其中$ω$在开放式$ \ mathbb {r}^d $的开放式集合中有所不同。虽然imimum的表征完全清楚，但在$ q> 1 $的情况下，最大化并没有发生同样的情况。我们证明，对于$ q $，足够大的Quasi Open集合中存在最大化的域，并且球在{\ IT几乎几乎是球形域}之间是最佳的。
We consider the shape optimization problems for the quantities $λ(Ω)T^q(Ω)$, where $Ω$ 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 {\it nearly spherical domains}.
