Abstract
AbstractWe consider shape functionals of the form $$F_q(\Omega )=P(\Omega )T^q(\Omega )$$
F
q
(
Ω
)
=
P
(
Ω
)
T
q
(
Ω
)
on the class of open sets of prescribed Lebesgue measure. Here $$q>0$$
q
>
0
is fixed, $$P(\Omega )$$
P
(
Ω
)
denotes the perimeter of $$\Omega $$
Ω
and $$T(\Omega )$$
T
(
Ω
)
is the torsional rigidity of $$\Omega $$
Ω
. The minimization and maximization of $$F_q(\Omega )$$
F
q
(
Ω
)
is considered on various classes of admissible domains $$\Omega $$
Ω
: in the class $$\mathcal {A}_{all}$$
A
all
of all domains, in the class $$\mathcal {A}_{convex}$$
A
convex
of convex domains, and in the class $$\mathcal {A}_{thin}$$
A
thin
of thin domains.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Control and Optimization
Cited by
10 articles.
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