Un nuovo approccio alle disuguaglianze isoperimetriche quantitative

Authors

  • Gian Paolo Leonardi Università di Modena - Reggio Emilia

DOI:

https://doi.org/10.6092/issn.2240-2829/2671

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.

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Published

2011-12-31

How to Cite

Leonardi, G. P. (2011). Un nuovo approccio alle disuguaglianze isoperimetriche quantitative. Bruno Pini Mathematical Analysis Seminar, 2(1). https://doi.org/10.6092/issn.2240-2829/2671

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