Sharp and quantitative bounds for torsional rigidity with Dirichlet and Robin boundary conditions

par Alba Lia Masiello (Université de Naples)

mardi 6 oct. 2026, 11:30 → 12:30 Europe/Paris

Carmes

Torsional rigidity is a classical quantity associated with the Poisson problem with
Dirichlet boundary conditions and is closely related to the geometry of the underlying
domain. In this talk we consider open, bounded and convex sets in R^n and present sharp
geometric inequalities relating torsional rigidity to basic geometric quantities such as the 
perimeter, the measure of the set, and the inradius. We also discuss quantitative versions of 
these inequalities, where the deficit from the optimal constant provides information on the
geometry of the optimal sequences. Finally, we address extensions of these results to 
torsional rigidity with Robin boundary conditions, focusing on the case of positive Robin 
parameter and highlighting the main similarities and differences with respect to the classical
Dirichlet setting.