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VAREG SIGNED

Variational approach to the regularity of the free boundaries

Total Cost €

0

EC-Contrib. €

0

Partnership

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Project "VAREG" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITA DI PISA 

Organization address
address: LUNGARNO PACINOTTI 43/44
city: PISA
postcode: 56126
website: www.unipi.it

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Italy [IT]
 Total cost 1˙330˙325 €
 EC max contribution 1˙330˙325 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2019-STG
 Funding Scheme ERC-STG
 Starting year 2020
 Duration (year-month-day) from 2020-06-01   to  2025-05-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITA DI PISA IT (PISA) coordinator 1˙330˙325.00

Map

 Project objective

The focus of this project is the regularity theory of free boundary problems. This is a fascinating topic, which combines methods from Analysis and Geometry, and has numerous applications to a large variety of problems in Physics, Engineering and Economy, which involve partial differential equations on domains whose boundary is free, that is, it is not a priori known. Typical examples are the Stefan problem, describing the evolution of a block of melting ice, and the American stock options. Since the shape of the boundary is free, it is a deep and usually extremely difficult question to study its fine structure. The regularity theory is precisely the art of deducing the local structure of the free boundary just by looking at a global energy-minimization property of the state function. In this project I aim to develop new techniques to study the regularity of the free boundaries and to give a precise description of the structure of the free boundaries around singular points. I will introduce a new variational method for the analysis of the free boundaries, aiming to solve several major open questions related to the classical one-phase, two-phase and the vectorial Bernoulli problems, the obstacle and thin-obstacle problems, which are the most important models both from a theoretical and applicative point of view. The techniques that I will develop in this project will have an impact on several domains, including the minimal surfaces, harmonic maps, free discontinuity problems, parabolic and non-local free boundary problems.

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The information about "VAREG" are provided by the European Opendata Portal: CORDIS opendata.

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