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RSPDE SIGNED

Regularity and Stability in Partial Differential Equations

Total Cost €

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EC-Contrib. €

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Partnership

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Project "RSPDE" data sheet

The following table provides information about the project.

Coordinator
EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH 

Organization address
address: Raemistrasse 101
city: ZUERICH
postcode: 8092
website: https://www.ethz.ch/de.html

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 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.

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