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SINGULARITY SIGNED

Singularities and Compactness in Nonlinear PDEs

Total Cost €

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EC-Contrib. €

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Partnership

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 SINGULARITY project word cloud

Explore the words cloud of the SINGULARITY project. It provides you a very rough idea of what is the project "SINGULARITY" about.

science    theorem    laws    solutions    guiding    hyperbolic    investigates    combine    connected    pi    microlocal    philippis    understand    parts    mathematical    equations    concerned    resolution    periodic    phenomena    condensated    instance    de    questions    powerful    conjecture    sequences    sources    theory    laminates    singular    heart    morrey    framework    singularities    tool    pde    nested    pioneering    structure    reaching    fundamental    building    vector    microstructure    employ    invented    forms    compensated    conservation    strategies    central    opened    microstructures    avenues    pressing    constrained    pdes    serve    nonlinear    tackle    led    optimization    lights    homogenization    shape    intriguing    tools    concentrations    dealing    singularity    theme    progress    material    solving    emergence    innovative    themes    asymptotic    fine    bouchitt    oscillations    relation    geometric    conjectures    inter    compactness    found    harmonic   

Project "SINGULARITY" data sheet

The following table provides information about the project.

Coordinator
THE UNIVERSITY OF WARWICK 

Organization address
address: Kirby Corner Road - University House
city: COVENTRY
postcode: CV4 8UW
website: www.warwick.ac.uk

contact info
title: n.a.
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surname: n.a.
function: n.a.
email: n.a.
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 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.

# participants  country  role  EC contrib. [€] 
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 ́e 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
List of publications.
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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