A sharp lower bound for torsional rigidity of convex domains

For every bounded convex domain Ω⊂ Rᵈ, d≥2, we establish the following sharp inequality for torsional rigidity T(Ω)≥2(d+1)/d∫_Ωdist(x,∂Ω)² x, where T(Ω)=4∫_Ωu x and $-Δu=1$ in $Ω$, u∈ H¹₀(Ω). Equality holds for balls.