SINGULARITY SIGNED
Singularities and Compactness in Nonlinear PDEs
Total Cost €
0EC-Contrib. €
0Partnership
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Explore the words cloud of the SINGULARITY project. It provides you a very rough idea of what is the project "SINGULARITY" about.
Project "SINGULARITY" data sheet
The following table provides information about the project.
| Coordinator |
THE UNIVERSITY OF WARWICK
Organization address contact info |
| Coordinator Country | United Kingdom [UK] |
| Project website | http://www.ercsingularity.org |
| Total cost | 1˙483˙943 € |
| EC max contribution | 1˙483˙943 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2017-STG |
| Funding Scheme | ERC-STG |
| Starting year | 2018 |
| Duration (year-month-day) | from 2018-04-01 to 2023-03-31 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | THE UNIVERSITY OF WARWICK | UK (COVENTRY) | coordinator | 1˙483˙943.00 |
Map
Project objective
The emergence of singularities, such as oscillations and concentrations, is at the heart of some of the most intriguing problems in the theory of nonlinear PDEs. Rich sources of these phenomena can be found for instance in the equations of mathematical material science and hyperbolic conservation laws.
Building on recent pioneering work of the PI, The SINGULARITY project will investigate singularities through innovative strategies and tools that combine geometric measure theory with harmonic analysis. The potential of this approach is far-reaching and has already led to the resolution of several long-standing conjectures as well as opened up new avenues to understand the fine structure of singularities.
The project comprises three inter-connected themes:
Theme I investigates condensated singularities, i.e. singular parts of (vector) measures solving a PDE. A powerful structure theorem was recently established by the PI and De Philippis, which will be developed into a fine structure theory for PDE-constrained measures.
Theme II is concerned with the development of a compensated compactness theory for sequences of solutions to a PDE, which is capable of dealing with concentrations. The central aim is to study in detail the (non-)compactness properties of such sequences in the presence of asymptotic singularities, for instance in relation to the Bouchitt Ìe Conjecture in shape optimization.
Theme III investigates higher-order microstructure, i.e. nested periodic oscillations in sequences, such as laminates. The main objective is to understand the effective properties of such microstructures and to make progress on pressing open problems in homogenization theory and on the fundamental Morrey Conjecture. We will employ the promising tool of microlocal compactness forms, recently invented by the PI.
All three themes tackle challenging and important open questions, which will serve as guiding lights towards a robust framework for the effective study of singularities.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2019 |
Adolfo Arroyo-Rabasa An elementary approach to the dimension of measures satisfying a first-order linear PDE constraint published pages: 1, ISSN: 0002-9939, DOI: 10.1090/proc/14732 |
Proceedings of the American Mathematical Society | 2019-10-29 |
| 2019 |
Adolfo Arroyo-Rabasa, Guido De Philippis, Jonas Hirsch, Filip Rindler Dimensional estimates and rectifiability for measures satisfying linear PDE constraints published pages: 639-658, ISSN: 1016-443X, DOI: 10.1007/s00039-019-00497-1 |
Geometric and Functional Analysis 29/3 | 2019-10-29 |
| 2019 |
Franz Gmeineder, Bogdan Raiţă Embeddings for A -weakly differentiable functions on domains published pages: 108278, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2019.108278 |
Journal of Functional Analysis 277/12 | 2019-10-29 |
| 2018 |
Guido De Philippis, Luca Palmieri, Filip Rindler On the two-state problem for general differential operators published pages: 387-396, ISSN: 0362-546X, DOI: 10.1016/j.na.2018.03.015 |
Nonlinear Analysis 177 | 2019-10-29 |
| 2019 |
Filip Rindler, Giles Shaw Liftings, Young Measures, and Lower Semicontinuity published pages: 1227-1328, ISSN: 0003-9527, DOI: 10.1007/s00205-018-01343-8 |
Archive for Rational Mechanics and Analysis 232/3 | 2019-10-29 |
| 2019 |
Bogdan Raiţă Critical $mathrm {L}^p$-differentiability of $mathrm {BV}^mathbb {A}$-maps and canceling operators published pages: 1, ISSN: 0002-9947, DOI: 10.1090/tran/7878 |
Transactions of the American Mathematical Society | 2019-10-29 |
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