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.
On two functionals involving the maximum of the torsion function / Henrot A.; Lucardesi I.; Philippin G.. - In: ESAIM. COCV. - ISSN 1292-8119. - STAMPA. - 24:(2018), pp. 1585-1604. [10.1051/cocv/2017069]
On two functionals involving the maximum of the torsion function
Lucardesi I.
;
2018
Abstract
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.
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