We introduce a new variational method for the study of isoperimetric inequalities with quantitative terms.The method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two notable applications are presented. First we give a new proof of the sharp quantitative isoperimetric inequality in R^n. Second we positively answer to a conjecture by Hall concerning the best constant for the quantitative isoperimetric inequality in R^2 in the small asymmetry regime.

A selection principle for the sharp quantitative isoperimetric inequality / Cicalese, Marco; Leonardi, Gian Paolo. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 2012, 206:2(2012), pp. 617-643. [10.1007/s00205-012-0544-1]

A selection principle for the sharp quantitative isoperimetric inequality

Leonardi Gian Paolo
2012-01-01

Abstract

We introduce a new variational method for the study of isoperimetric inequalities with quantitative terms.The method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two notable applications are presented. First we give a new proof of the sharp quantitative isoperimetric inequality in R^n. Second we positively answer to a conjecture by Hall concerning the best constant for the quantitative isoperimetric inequality in R^2 in the small asymmetry regime.
2012
2
Cicalese, Marco; Leonardi, Gian Paolo
A selection principle for the sharp quantitative isoperimetric inequality / Cicalese, Marco; Leonardi, Gian Paolo. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 2012, 206:2(2012), pp. 617-643. [10.1007/s00205-012-0544-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/229221
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