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

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.

Fields of science (EuroSciVoc)

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Keywords

Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)

Programme(s)

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Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

ERC-STG - Starting Grant

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Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

(opens in new window) ERC-2018-STG

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Host institution

UNIVERSITAT DE BARCELONA
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 950 306,25
Address
GRAN VIA DE LES CORTS CATALANES 585
08007 BARCELONA
Spain

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Region
Este Cataluña Barcelona
Activity type
Higher or Secondary Education Establishments
Links
Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 950 306,25

Beneficiaries (2)

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