Objective
Singular solutions to variational problems and to partial differential equations are naturally ubiquitous in many contexts, and among these minimal surfaces theory and free boundary problems are two prominent examples both for their analytical content and their physical interest.
A crucial aspect in this regard is the co-dimension of the objects under consideration: indeed, many of the analytical and geometric principles which are valid for minimal hypersurfaces or regular points of the free boundary do not apply to higher co-dimension surfaces or singular free boundary points.
The aim of this project is to investigate some of the most compelling questions about the singularities of two classical problems in the geometric calculus of variations in higher co-dimension:
I. Mass-minimizing integer rectifiable currents, i.e. solutions to the Plateau problem of finding the surfaces of least area, attacking specific conjectures about the structure of the singular set, most prominently the boundedness of its measure.
II. The thin obstacle problem, consisting in minimizing the Dirichlet energy (or a variant of it) among functions constrained above an obstacle that is assigned on a lower dimensional space, with the purpose of answering some of the main open questions on the singular free boundary points.
The main unifying theme of the project is the central role played by geometric measure theory, which underlines various common aspects of these two problems and makes them suited to be treated in an unified framework.
Although these are classical questions with a long tradition, our knowledge about them is still limited and their investigation is among the most challenging issues in regularity theory. This is the central focus of the project, with the final goal to develop suitable analytical techniques that provides valuable insights on the mathematics at the basis of higher co-dimension singularities, eventually fruitful in other geometric and analytical settings.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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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)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
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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.
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.
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.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2017-STG
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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.
00185 Roma
Italy
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.