Abstract
In this paper we investigate upper and lower bounds of two shape functionals involving the maximum of the torsion function. More precisely, we considerT(Ω)∕(M(Ω)|Ω|) andM(Ω)λ1(Ω), whereΩis a bounded open set of ℝdwith finite Lebesgue measure |Ω|,M(Ω) denotes the maximum of the torsion function,T(Ω) the torsion, andλ1(Ω) the first Dirichlet eigenvalue. Particular attention is devoted to the subclass of convex sets.
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