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On a reverse Kohler-Jobin inequality
Authors
Serena Guarino Lo Bianco
Luca Briani
Giuseppe Buttazzo
Publication date
10 December 2022
Publisher
View
on
arXiv
Abstract
We consider the shape optimization problems for the quantities
λ
(
Ω
)
T
q
(
Ω
)
\lambda(\Omega)T^q(\Omega)
λ
(
Ω
)
T
q
(
Ω
)
, where
Ω
\Omega
Ω
varies among open sets of
R
d
\mathbb{R}^d
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
q>1
q
>
1
. We prove that for
q
q
q
large enough a maximizing domain exists among quasi-open sets and that the ball is optimal among {\it nearly spherical domains}
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oai:arXiv.org:2212.05375
Last time updated on 08/01/2023