On two functionals involving the maximum of the torsion function
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1585-1604.

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 ) λ 1 ( Ω ) , where Ω is a bounded open set of d with finite Lebesgue measure Ω , M ( Ω ) denotes the maximum of the torsion function, T ( Ω ) the torsion, and λ 1 ( Ω ) the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.

DOI : 10.1051/cocv/2017069
Classification : 35P15, 49R05, 35J25, 35B27, 49Q10
Mots clés : Torsional rigidity, first Dirichlet eigenvalue, shape optimization
Henrot, Antoine 1 ; Lucardesi, Ilaria 1 ; Philippin, Gérard 1

1
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Henrot, Antoine; Lucardesi, Ilaria; Philippin, Gérard. On two functionals involving the maximum of the torsion function. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 4, pp. 1585-1604. doi : 10.1051/cocv/2017069. http://archive.numdam.org/articles/10.1051/cocv/2017069/

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