Objectif "This project focuses on several problems in Partial Differential Equations (PDEs) and the Calculus of Variations. These include:- Optimal transport and Monge-Ampère equations.In the last 30 years, the optimal transport problem has been found to be useful to several areasof mathematics. In particular, this problem is related to Monge-Ampère type equations, and understanding the regularity properties of solutions to such equations is an important question with applications to several other fields.- Stability in functional and geometric inequalities.Whether a minimizer of some inequality is ""stable'' in some suitable senseis an important issue in order to understand and/or predict the evolution in time of a physical phenomenon.For instance, quantitative stability results allow one to quantify the rate of convergence of a physical system to some steady state, and they can also be used to understand how much the system changes under the influence of exterior factors.- Di Perna-Lions theory and PDEs.The study of transport equations with rough coefficients is a very active research area. In particular, recent developments have been used to obtain new results on the semiclassical limit for the Schr\""odinger equation and on the Lagrangian structure of transport equations with singular vector-fields (for instance, the Vlasov-Poisson equation). These problems, although apparently different, are actually deeply interconnected.The PI aims to use his expertise in partial differential equations and geometric measure theory to introduce ideas and techniques that will lead to new groundbreaking results." Champ scientifique natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations Mots‑clés RSPDE Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-2016-COG - ERC Consolidator Grant Appel à propositions ERC-2016-COG Voir d’autres projets de cet appel Régime de financement ERC-COG - Consolidator Grant Institution d’accueil EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH Contribution nette de l'UE € 1 742 428,00 Adresse Raemistrasse 101 8092 Zuerich Suisse Voir sur la carte Région Schweiz/Suisse/Svizzera Zürich Zürich Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 742 428,00 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH Suisse Contribution nette de l'UE € 1 742 428,00 Adresse Raemistrasse 101 8092 Zuerich Voir sur la carte Région Schweiz/Suisse/Svizzera Zürich Zürich Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 742 428,00