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Financement de l’UE (1 483 943 €) : Singularités et compacité dans les EDP non linéaires Hor 24/01/2018 Programme de recherche et d'innovation de l'UE « Horizon »
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Singularités et compacité dans les EDP non linéaires
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.
| University of Warwick | 1 483 943 € |
https://cordis.europa.eu/project/id/757254
Cette annonce se réfère à une date antérieure et ne reflète pas nécessairement l’état actuel. L’état actuel est présenté à la page suivante : University of Warwick, CV 4 7AL Coventry, Royaume Uni.
