ANOPTSETCON

Analysis of optimal sets and optimal constants: old questions and new results

 Coordinatore FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG 

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 Nazionalità Coordinatore Germany [DE]
 Totale costo 540˙000 €
 EC contributo 540˙000 €
 Programma FP7-IDEAS-ERC
Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
 Code Call ERC-2010-StG_20091028
 Funding Scheme ERC-SG
 Anno di inizio 2010
 Periodo (anno-mese-giorno) 2010-08-01   -   2015-07-31

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITA DEGLI STUDI DI PAVIA

 Organization address address: STRADA NUOVA 65
city: PAVIA
postcode: 27100

contact info
Titolo: Dr.
Nome: Simona
Cognome: Albini
Email: send email
Telefono: +39 382 985557
Fax: +39 382 985603

IT (PAVIA) beneficiary 132˙879.00
2    UNIVERSITA DEGLI STUDI DI FIRENZE

 Organization address address: Piazza San Marco 4
city: Florence
postcode: 50121

contact info
Titolo: Dr.
Nome: Patrizia
Cognome: Cecchi
Email: send email
Telefono: +39 055 4598694
Fax: +39 055 4598694

IT (Florence) beneficiary 15˙077.00
3    FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG

 Organization address address: SCHLOSSPLATZ 4
city: ERLANGEN
postcode: 91054

contact info
Titolo: Ms.
Nome: Kathrin
Cognome: Linz-Dinchel
Email: send email
Telefono: +49 9131 8526471
Fax: +49 9131 8526239

DE (ERLANGEN) hostInstitution 392˙044.00
4    FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG

 Organization address address: SCHLOSSPLATZ 4
city: ERLANGEN
postcode: 91054

contact info
Titolo: Prof.
Nome: Aldo
Cognome: Pratelli
Email: send email
Telefono: +49 9131 8567048
Fax: +49 9131 8567047

DE (ERLANGEN) hostInstitution 392˙044.00

Mappa


 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

answer    ball    proved    volume    inequalities    geometric    years    questions    natural    last    sobolev    constants    perimeter    techniques    tools    optimal    question    minimizes    sharp    functional   

 Obiettivo del progetto (Objective)

'The analysis of geometric and functional inequalities naturally leads to consider the extremal cases, thus looking for optimal sets, or optimal functions, or optimal constants. The most classical examples are the (different versions of the) isoperimetric inequality and the Sobolev-like inequalities. Much is known about equality cases and best constants, but there are still many questions which seem quite natural but yet have no answer. For instance, it is not known, even in the 2-dimensional space, the answer of a question by Brezis: which set, among those with a given volume, has the biggest Sobolev-Poincaré constant for p=1? This is a very natural problem, and it appears reasonable that the optimal set should be the ball, but this has never been proved. The interest in problems like this relies not only in the extreme simplicity of the questions and in their classical flavour, but also in the new ideas and techniques which are needed to provide the answers. The main techniques that we aim to use are fine arguments of symmetrization, geometric constructions and tools from mass transportation (which is well known to be deeply connected with functional inequalities). These are the basic tools that we already used to reach, in last years, many results in a specific direction, namely the search of sharp quantitative inequalities. Our first result, together with Fusco and Maggi, showed what follows. Everybody knows that the set which minimizes the perimeter with given volume is the ball. But is it true that a set which almost minimizes the perimeter must be close to a ball? The question had been posed in the 1920's and many partial result appeared in the years. In our paper (Ann. of Math., 2007) we proved the sharp result. Many other results of this kind were obtained in last two years.'

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