46 citations · 91 across the 17 of their papers we have counts for
4 papers · 1 filter
Sharp bounds for the p-torsion of convex planar domains
Ilaria Fragalà, Filippo Gazzola, Jimmy Lamboley
We obtain some sharp estimates for the -torsion of convex planar domains in terms of their area, perimeter, and inradius. The approach we adopt relies on the use of web function…
Regularity and singularities of Optimal Convex shapes in the plane
Jimmy Lamboley, Michel Pierre, Arian Novruzi
We focus here on the analysis of the regularity or singularity of solutions $\Om_{0}$ to shape optimization problems among convex planar sets, namely: $$ J(\Om_{0})=\min\{J(\Om),\…
On the local minimizers of the Mahler volume
Evans Harrell, Antoine Henrot, Jimmy Lamboley
We focus on the analysis of local minimizers of the Mahler volume, that is to say the local solutions to the problem $$\min\{ M(K):=|K||K^\circ|\;/\;K\subset\R^d\textrm{ open and c…
Optimal convex shapes for concave functionals
Dorin Bucur, Ilaria Fragalà, Jimmy Lamboley
Motivated by a long-standing conjecture of Polya and Szegö about the Newtonian capacity of convex bodies, we discuss the role of concavity inequalities in shape optimization, and w…