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EllipticPDE SIGNED

Regularity and singularities in elliptic PDE's: beyond monotonicity formulas

Total Cost €

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EC-Contrib. €

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Partnership

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Project "EllipticPDE" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAT ZURICH 

Organization address
address: RAMISTRASSE 71
city: ZURICH
postcode: 8006
website: n.a.

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 Switzerland [CH]
 Total cost 1˙335˙250 €
 EC max contribution 1˙335˙250 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2018-STG
 Funding Scheme ERC-STG
 Starting year 2019
 Duration (year-month-day) from 2019-01-01   to  2023-12-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT ZURICH CH (ZURICH) coordinator 1˙335˙250.00

Map

 Project objective

One of the oldest and most important questions in PDE theory is that of regularity. A classical example is Hilbert's XIXth problem (1900), solved by De Giorgi and Nash in 1956. During the second half of the XXth century, the regularity theory for elliptic and parabolic PDE's experienced a huge development, and many fundamental questions were answered by Caffarelli, Nirenberg, Krylov, Evans, Nadirashvili, Friedman, and many others. Still, there are problems of crucial importance that remain open.

The aim of this project is to go significantly beyond the state of the art in some of the most important open questions in this context. In particular, three key objectives of the project are the following. First, to introduce new techniques to obtain fine description of singularities in nonlinear elliptic PDE's. Aside from its intrinsic interest, a good regularity theory for singular points is likely to provide insightful applications in other contexts. A second aim of the project is to establish generic regularity results for free boundaries and other PDE problems. The development of methods which would allow one to prove generic regularity results may be viewed as one of the greatest challenges not only for free boundary problems, but for PDE problems in general. Finally, the third main objective is to achieve a complete regularity theory for nonlinear elliptic PDE's that does not rely on monotonicity formulas. These three objectives, while seemingly different, are in fact deeply interrelated.

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

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