Project description
A variational principle to the regularity of free boundary problems
Free boundary problems, which involve a partial differential equation on a domain whose boundary is free, naturally arise in many different models in physics, engineering and economy. The EU-funded VAREG project plans to study free boundary problems from a purely theoretical point of view. The focus will be on the regularity of the free boundaries arising in the context of variational minimisation problems such as the one-phase, the two-phase and the vectorial Bernoulli problems as well as the obstacle and thin-obstacle problems. The project will develop new techniques for analysing the fine structure of the free boundaries, especially around singularities. Many tools and methods developed can find application in other problems and domains, including area-minimising surfaces, harmonic maps, free-discontinuity problems and parabolic and non-local free boundary problems.
Objective
The focus of this project is the regularity theory of free boundary problems. This is a fascinating topic, which combines methods from Analysis and Geometry, and has numerous applications to a large variety of problems in Physics, Engineering and Economy, which involve partial differential equations on domains whose boundary is free, that is, it is not a priori known. Typical examples are the Stefan problem, describing the evolution of a block of melting ice, and the American stock options. Since the shape of the boundary is free, it is a deep and usually extremely difficult question to study its fine structure. The regularity theory is precisely the art of deducing the local structure of the free boundary just by looking at a global energy-minimization property of the state function. In this project I aim to develop new techniques to study the regularity of the free boundaries and to give a precise description of the structure of the free boundaries around singular points. I will introduce a new variational method for the analysis of the free boundaries, aiming to solve several major open questions related to the classical one-phase, two-phase and the vectorial Bernoulli problems, the obstacle and thin-obstacle problems, which are the most important models both from a theoretical and applicative point of view. The techniques that I will develop in this project will have an impact on several domains, including the minimal surfaces, harmonic maps, free discontinuity problems, parabolic and non-local free boundary problems.
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.
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
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.
-
H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC)
MAIN PROGRAMME
See all projects funded under this programme
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
See all projects funded under this funding scheme
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-2019-STG
See all projects funded under this callHost institution
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.