RSPDE SIGNED
Regularity and Stability in Partial Differential Equations
Total Cost €
0EC-Contrib. €
0Partnership
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Project "RSPDE" data sheet
The following table provides information about the project.
| Coordinator |
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Organization address contact info |
| Coordinator Country | Switzerland [CH] |
| Total cost | 1˙742˙428 € |
| EC max contribution | 1˙742˙428 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2016-COG |
| Funding Scheme | ERC-COG |
| Starting year | 2017 |
| Duration (year-month-day) | from 2017-02-01 to 2022-01-31 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH | CH (ZUERICH) | coordinator | 1˙742˙428.00 |
Map
Project objective
'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 areas of 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 sense is 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. '
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2019 |
Dario Cordero-Erausquin, Alessio Figalli Regularity of monotone transport maps between unbounded domains published pages: 7101-7112, ISSN: 1553-5231, DOI: 10.3934/dcds.2019297 |
Discrete & Continuous Dynamical Systems - A 39/12 | 2020-02-19 |
| 2019 |
Luigi Ambrosio, Federico Glaudo, Dario Trevisan On the optimal map in the $ 2 $-dimensional random matching problem published pages: 7291-7308, ISSN: 1553-5231, DOI: 10.3934/dcds.2019304 |
Discrete & Continuous Dynamical Systems - A 39/12 | 2020-02-19 |
| 2018 |
Yash Jhaveri On the (In)stability of the Identity Map in Optimal Transportation published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli On the Continuity of Center-Outward Distribution and Quantile Functions published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Connor Mooney The Monge-Ampère Equation published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Connor Mooney Singularities of complex-valued solutions to linear parabolic equations published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli Regularity of interfaces in phase transitions via obstacle problems published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli, Joaquim Serra On the fine structure of the free boundary for the classical obstacle problem published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Xavier Fernández-Real, Yash Jhaveri On the singular set in the thin obstacle problem: higher order blow-ups and the very thin obstacle problem published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2019 |
Xavier Fernández-Real, Xavier Ros-Oton On global solutions to semilinear elliptic equations related to the one-phase free boundary problem published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Connor Mooney, Ovidiu Savin REGULARITY RESULTS FOR THE EQUATION u11u22 = 1 published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli, Moon-Jin Kang A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli, Joaquim Serra On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1 published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Xavier Fernánder-Real, Joaquim Serra Regularity of minimal surfaces with lower dimensional obstacles published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli On the Monge-Ampère equation published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Alessio Figalli Free boundary regularity in obstacle problems published pages: , ISSN: , DOI: |
2019-09-09 | |
| 2018 |
Xavier Fernández-Real The Lagrangian Structure of the Vlasov–Poisson System in Domains with Specular Reflection published pages: 1327-1406, ISSN: 0010-3616, DOI: 10.1007/s00220-018-3242-5 |
Communications in Mathematical Physics 364/3 | 2019-08-29 |
| 2018 |
Jhaveri, Yash Regularity Results for Generated Jacobian Equations published pages: , ISSN: , DOI: 10.3929/ethz-b-000274281 |
3 | 2019-08-29 |
| 2018 |
Matteo Bonforte, Alessio Figalli, Juan Luis Vázquez Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-018-1321-2 |
Calculus of Variations and Partial Differential Equations 57/2 | 2019-04-25 |
| 2017 |
Tristan C. Collins, Connor Mooney Dimension of the minimum set for the real andcomplex Monge–Ampère equations in critical Sobolev spaces published pages: 2031-2041, ISSN: 2157-5045, DOI: 10.2140/apde.2017.10.2031 |
Analysis & PDE 10/8 | 2019-04-25 |
| 2018 |
Sylvia Serfaty, Joaquim Serra Quantitative stability of the free boundary in the obstacle problem published pages: 1803-1839, ISSN: 2157-5045, DOI: 10.2140/apde.2018.11.1803 |
Analysis & PDE 11/7 | 2019-04-25 |
| 2018 |
Xavier Fernández-Real, Xavier Ros-Oton The obstacle problem for the fractional Laplacian with critical drift published pages: 1683-1735, ISSN: 0025-5831, DOI: 10.1007/s00208-017-1600-9 |
Mathematische Annalen 371/3-4 | 2019-04-25 |
| 2018 |
Matteo Bonforte, Alessio Figalli, Juan Luis Vázquez Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains published pages: 945-982, ISSN: 2157-5045, DOI: 10.2140/apde.2018.11.945 |
Analysis & PDE 11/4 | 2019-04-25 |
| 2017 |
Yash Jhaveri Partial regularity of solutions to the second boundary value problem for generated Jacobian equations published pages: 445-476, ISSN: 1073-2772, DOI: 10.4310/MAA.2017.v24.n4.a2 |
Methods and Applications of Analysis 24/4 | 2019-04-25 |
| 2017 |
Xavier Fernández-Real, Xavier Ros-Oton Regularity theory for general stable operators: Parabolic equations published pages: 4165-4221, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2017.02.015 |
Journal of Functional Analysis 272/10 | 2019-04-25 |
| 2018 |
Alessio Figalli, Connor Mooney An Obstacle Problem for Conical Deformations of Thin Elastic Sheets published pages: 401-429, ISSN: 0003-9527, DOI: 10.1007/s00205-017-1195-z |
Archive for Rational Mechanics and Analysis 228/2 | 2019-04-25 |
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