Codice  QDD 117 
Titolo  Sharp bounds for the ptorsion of convex planar domains 
Data  20120131 
Autore/i  Fragalà, I.; Gazzola, F.; Lamboley, J. 
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Abstract  We obtain some sharp estimates for the ptorsion 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 ptorsion among polygons having a given number of vertices and a given area. A longstanding conjecture by P´olyaSzeg¨o 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. 
