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.

UN NUOVO APPROCCIO ALLE DISUGUAGLIANZE ISOPERIMETRICHE QUANTITATIVE / Leonardi, Gian Paolo. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - ELETTRONICO. - 1:(2011), pp. 1-15. [10.6092/issn.2240-2829/2671]

UN NUOVO APPROCCIO ALLE DISUGUAGLIANZE ISOPERIMETRICHE QUANTITATIVE

LEONARDI, Gian Paolo
2011

Abstract

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.
2011
1
1
15
UN NUOVO APPROCCIO ALLE DISUGUAGLIANZE ISOPERIMETRICHE QUANTITATIVE / Leonardi, Gian Paolo. - In: BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR. - ISSN 2240-2829. - ELETTRONICO. - 1:(2011), pp. 1-15. [10.6092/issn.2240-2829/2671]
Leonardi, Gian Paolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/825689
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