On the stability of the annulus for the torsion of multiply connected domains
Abstract
Abstract We establish a quantitative version of the isoperimetric inequality for the torsional rigidity of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we study how a domain approaches an annular configuration when its torsional rigidity is close to optimal. Our result shows that when the torsional rigidity is nearly optimal, the domain $$\Omega $$ Ω must be close to an annulus.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Analytic and geometric function theory
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 6
- Publication date
- 1 June 2026
- Language
- EN