Sharp bounds for the p-torsion of convex planar domains - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2013

Sharp bounds for the p-torsion of convex planar domains

Résumé

We obtain some sharp estimates for the $p$-torsion of convex planar domains in terms of their area, perimeter, and inradius. The approach we adopt relies on the use of web functions (i.e. functions depending only on the distance from the boundary), and on the behaviour of the inner parallel sets of convex polygons. As an application of our isoperimetric inequalities, we consider the shape optimization problem which consists in maximizing the $p$-torsion among polygons having a given number of vertices and a given area. A long-standing conjecture by Pólya-Szegö states that the solution is the regular polygon. We show that such conjecture is true within the subclass of polygons for which a suitable notion of ''asymmetry measure'' exceeds a critical threshold.
Fichier principal
Vignette du fichier
IFFGJL.pdf (131.08 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00654228 , version 1 (21-12-2011)

Identifiants

Citer

Ilaria Fragalà, Filippo Gazzola, Jimmy Lamboley. Sharp bounds for the p-torsion of convex planar domains. Geometric Properties for Parabolic and Elliptic PDE's, Jun 2011, Italy. pp.97-115. ⟨hal-00654228⟩
115 Consultations
98 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More