Project description
Time to theoretically analyse free interfaces
Free boundaries and interfaces arise in partial differential equations and the calculus of variations, where solutions and domains evolve. They are observed in phenomena, such as phase transitions, water waves, jet flows, tumour growth, and crowd motion. The ERC-funded FiRM project aims to analyse free interfaces theoretically by exploring Regularity Theory. It will explore a weak definition of a solution, without assumptions about the domain’s shape or topology, to describe the local structure of the free boundary and its evolution. It will focus on the formation and persistence of singularities in space and time. The project will develop analytical methods for understanding free interfaces near these singularities, with implications for partial differential equations and geometric analysis.
Objective
Free boundaries and interfaces arise in problems in PDEs and Calculus of Variations, in which both the solutions and their domains are free to evolve in time. Several physical models and phenomena naturally lead to the formation of free boundaries and interfaces, for instance, phase-transition (the Stefan problems), periodic water waves (Stokes water waves), jet flows (the Bernoulli problems), tumor growth and congested crowd motion (Hele-Shaw flows), strong segregation (optimal partitions; harmonic maps).
This project is dedicated to the analysis of the free interfaces from a purely theoretical point of view.
The focus is on the Regularity Theory: starting from some very weak notion of solution and without making any a priori assumption on the shape and on the topology of its domain, we aim to describe the local structure of the free boundary and its evolution in time. Two phenomena will be central for the project: the formation of singularities in space and the persistence of these singularities in time. My main objective is to develop analytic methods for the description of the local structure of the free interfaces around such singularities. These results will have broad impact on the fields of PDEs and Geometric 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 topology
- 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)
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Topic(s)
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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-2025-COG
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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
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