We introduce a new variational method for studying geometric and functional inequalities with quantitative terms. In the context of isoperimetric-type inequalities, this method (called Selection Principle) is based on a penalization technique combined with the regularity theory of quasiminimizers of the perimeter functional. In this seminar we present the method and describe two remarkable applications. The rst one is a new proof of the sharp quantitative isoperimetric inequality in Rn. The second one is the proof of a conjecture posed by Hall about the optimal constant in the quantitative isoperimetric inequality in R2, in the small asymmetry regime.
@article{2671,
title = {Un nuovo approccio alle disuguaglianze isoperimetriche quantitative},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2011},
doi = {10.6092/issn.2240-2829/2671},
language = {IT},
url = {http://dml.mathdoc.fr/item/2671}
}
Leonardi, Gian Paolo. Un nuovo approccio alle disuguaglianze isoperimetriche quantitative. Bruno Pini Mathematical Analysis Seminar, (2011), . doi : 10.6092/issn.2240-2829/2671. http://gdmltest.u-ga.fr/item/2671/