On two functionals involving the maximum of the torsion function

A Henrot (1) , Ilaria Lucardesi (1) , G Philippin (2)

1 IECL - Institut Élie Cartan de Lorraine
2 ULaval - Université Laval [Québec]

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 R 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.

Mots clés: torsional rigidity; shape optimization; first Dirichlet eigenvalue

Domaines: Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

A Henrot, Ilaria Lucardesi, G Philippin. On two functionals involving the maximum of the torsion function. ESAIM: Control, Optimisation and Calculus of Variations, 2018, 24 (4), pp.1585-1604. ⟨10.1051/cocv/2017069⟩. ⟨hal-01453470v2⟩