Objective
The interaction between microscopic and macroscopic quantities lies at the heart of fascinating problems in the modern theory of nonlinear PDEs. This phenomenon, modeled by weak forms of convergence, entails the formation of oscillations, concentrations, and fine geometric patterns ubiquitous in geometric, physical, and materials science models. ConFine will investigate the nature of concentrations and fine geometries arising from longstanding conjectures and novel questions of the calculus of variations. The goals comprise two themes. Theme I examines the qualitative and quantitative nature of PDE-constrained concentrations. Building upon results recently pioneered by the PI, its purpose is to prove a novel interpretation of Bouchitte's Vanishing mass conjecture, and novel compensated integrability results, with profound implications for the compensated compactness theory. Theme II investigates the fine properties of PDE-constrained measures from three different perspectives. Via potential and measure theory methods, it will attempt to produce substantial advances towards solving the sigma-finiteness conjecture in BD spaces. It will also investigate the structure integral of varifolds with bounded first-variation. The goal is to prove that these measure-theoretic generalizations of surfaces possess an underlying BV-like structure. Lastly, Theme II conjectures a complementary result to the ground-breaking De Philippis--Rindler theorem, which asserts that the regular part of an A-free measure is essentially unconstrained. This set of problems comprises significant theoretical obstacles at the forefront of the calculus of variations and geometric measure theory. In this regard, the proposed methodology gathers novel ideas oriented to overcome such paramount challenges. Consequently, far-reaching implications beyond the proposed objectives are expected, in the development of new methods and applications, in diverse fields of Analysis.
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 geometry
- 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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HORIZON.1.1 - 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.
HORIZON-ERC - HORIZON ERC Grants
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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-2022-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.
56126 PISA
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.