论文标题
一些涉及周长和扭转僵硬的不平等现象
Some inequalities involving perimeter and torsional rigidity
论文作者
论文摘要
我们考虑$ f_q（ω）= p（ω）t^q（ω）$的形状功能。这里$ q> 0 $是固定的，$ p（ω）$表示$ω$，$ t（ω）$的周长是$ω$的扭转刚度。 $ f_q（ω）$的最小化和最大化在各种可允许的域$ω$上考虑：在类$ \ Mathcal {a} _ {a} _ {All域中，在类$ \ Mathcal {a} _} _ {convex} $ tint $ convex $ tint y Math y Math in Clast $ \ Mathcal {a} _域。
We consider shape functionals of the form $F_q(Ω)=P(Ω)T^q(Ω)$ on the class of open sets of prescribed Lebesgue measure. Here $q>0$ is fixed, $P(Ω)$ denotes the perimeter of $Ω$ and $T(Ω)$ is the torsional rigidity of $Ω$. The minimization and maximization of $F_q(Ω)$ is considered on various classes of admissible domains $Ω$: in the class $\mathcal{A}_{all}$ of all domains, in the class $\mathcal{A}_{convex}$ of convex domains, and in the class $\mathcal{A}_{thin}$ of thin domains.
