Project description
Rethinking non-linear equations
Partial differential equations (PDEs) are the language of physical systems. PDEs are central in the modelling of complex phenomena such as fluid flow, wave propagation, heat transfer, electromagnetism and elasticity. A crucial aspect is the (ir)regularity of solutions, which is fundamental for describing their qualitative properties. The ERC-funded NEW project is pushing the boundaries of the analysis of non-linear equations by addressing key regularity challenges in settings where classical theory fails. Achievements include sharp analysis data/solutions in nonuniformly elliptic or parabolic PDEs, maximal regularity for degenerate or nonlocal operators and singular set estimates in vectorial problems. Beyond theoretical advances, the outcome will transform techniques and perspectives developed through half a century of progress in non-linear regularity theory.
Objective
Project NEW tackles key challenges in nonlinear elliptic and parabolic regularity theory. The outcome answers to fundamental open questions. Achievements include sharp analysis data-solutions in nonuniformly elliptic or parabolic PDEs, singular set estimates in vectorial problems, and maximal regularity in degenerate (possibly nonlocal) monotone operators lacking strong monotonicity properties. These results are supported by innovative hybrid techniques, combining deep insights from harmonic analysis, nonlinear potential theory, and variational analysis, specifically devised to be implemented directly at the PDE level. Beyond technical and theoretical advances, the accomplishments will significantly impact Non-Newtonian fluid mechanics, homogenization, and geometric analysis, transforming techniques and perspectives developed through half a century of progress in nonlinear regularity theory.
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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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-2025-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.
43121 PARMA
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.