On the optimal sets in Polya and Makai type inequalities
In this paper, we examine some shape functionals, introduced by P\'olya and Makai, involving the torsional rigidity and the first Dirichlet-Laplacian eigenvalue for bounded, open and convex sets of $\R^n$. We establish quantitative bounds, which give us key properties and information on the behavior of the optimizing sequences. In particular, we consider two kinds of reminder terms that provide information about the structure of these minimizing sequences, such as information about the thickness.
Authors
- Rossano Sannipoli (ORCID: https://orcid.org/0000-0002-5161-9044)
- Nunzia Gavitone (ORCID: https://orcid.org/0000-0002-1393-7084)
- Vincenzo Amato (ORCID: https://orcid.org/0000-0002-9422-5651)
Publication Details
- Journal
- ESAIM Control Optimisation and Calculus of Variations
- Published
- 2026-06-09
- DOI
- https://doi.org/10.1051/cocv/2026038
- Primary Topic
- Mathematical Inequalities and Applications
- Type
- preprint
- Field-Weighted Citation Impact
- 0.00
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni