Volume 24, Number 4, October–December 2018
|Page(s)||1585 - 1604|
|Published online||10 December 2018|
On two functionals involving the maximum of the torsion function
InstitutÉlie Cartan de Lorraine, UMR 7502, Université de Lorraine CNRS,
Vandoeuvre les Nancy Cedex, France
2 Département de Mathématiques, Université Laval Québec, Québec, QC G1V 0A6, Canada
* Corresponding author: firstname.lastname@example.org
Accepted: 14 October 2017
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we consider T(Ω)∕(M(Ω)|Ω|) and M(Ω)λ1(Ω), where Ω is a bounded open set of ℝd with finite Lebesgue measure |Ω|, M(Ω) denotes the maximum of the torsion function, T(Ω) the torsion, and λ1(Ω) the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.
Mathematics Subject Classification: 35P15 / 49R05 / 35J25 / 35B27 / 49Q10
Key words: Torsional rigidity / first Dirichlet eigenvalue / shape optimization
© EDP Sciences, SMAI 2018
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