ANOPTSETCON
Analysis of optimal sets and optimal constants: old questions and new results
| Coordinatore | FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| 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
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITA DEGLI STUDI DI PAVIA
Organization address
address: STRADA NUOVA 65 contact info |
IT (PAVIA) | beneficiary | 132˙879.00 |
| 2 |
UNIVERSITA DEGLI STUDI DI FIRENZE
Organization address
address: Piazza San Marco 4 contact info |
IT (Florence) | beneficiary | 15˙077.00 |
| 3 |
FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG
Organization address
address: SCHLOSSPLATZ 4 contact info |
DE (ERLANGEN) | hostInstitution | 392˙044.00 |
| 4 |
FRIEDRICH-ALEXANDER-UNIVERSITAT ERLANGEN NURNBERG
Organization address
address: SCHLOSSPLATZ 4 contact info |
DE (ERLANGEN) | hostInstitution | 392˙044.00 |
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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.'