Regularity and Stability in Partial Differential Equations

Project Information

RSPDE

Grant agreement ID: 721675

DOI

10.3030/721675

Project closed

EC signature date 2 December 2016

Start date 1 February 2017

End date 31 July 2023

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 742 428,00

EU contribution

€ 1 742 428,00

Coordinated by

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Switzerland

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (24)

Free boundary partial regularity in the thin obstacle problem

Author(s): Federico Franceschini, Joaquim Serra
Published in: Communications on Pure and Applied Mathematics, 2021, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.

Local existence of smooth solutions for the semigeostrophic equations on curved domains

Author(s): Lauro Silini
Published in: SIAM J. Math. Anal., 2022, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics

A Faber–Krahn inequality for Wavelet transforms

Author(s): João P. G. Ramos; Paolo Tilli
Published in: Bulletin of the London Mathematical Society, Issue 6, 2022, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.12833

Minkowski inequality for nearly spherical domains

Author(s): F. Glaudo
Published in: Advances in Mathematics, 408 (Part B), Issue 7, 2021, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108595

Uniqueness of Solutions to Nonlinear Schrödinger Equations from their Zeros

Author(s): Christoph Kehle; João P. G. Ramos
Published in: Annals of PDE, 8 (2), Issue 2, 2022, ISSN 2199-2576
Publisher: Springer
DOI: 10.1007/s40818-022-00138-1

Regularity properties of monotone measure-preserving maps

Author(s): Alessio Figalli; Yash Jhaveri
Published in: Advanced nonlinear studies, 23 (1), Issue 4, 2023, ISSN 1536-1365
Publisher: UTHSCSA Press
DOI: 10.1515/ans-2022-0057

Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains

Author(s): Matteo Bonforte, Alessio Figalli, Juan Luis Vázquez
Published in: Analysis & PDE, Issue 11/4, 2018, Page(s) 945-982, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2018.11.945

An Obstacle Problem for Conical Deformations of Thin Elastic Sheets

Author(s): Alessio Figalli, Connor Mooney
Published in: Archive for Rational Mechanics and Analysis, Issue 228/2, 2018, Page(s) 401-429, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-017-1195-z

Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations

Author(s): Matteo Bonforte, Alessio Figalli, Juan Luis Vázquez
Published in: Calculus of Variations and Partial Differential Equations, Issue 57/2, 2018, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-018-1321-2

Dimension of the minimum set for the real and complex Monge–Ampère equations in critical Sobolev spaces

Author(s): Tristan C. Collins, Connor Mooney
Published in: Analysis & PDE, Issue 10/8, 2017, Page(s) 2031-2041, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2017.10.2031

Partial regularity of solutions to the second boundary value problem for generated Jacobian equations

Author(s): Yash Jhaveri
Published in: Methods and Applications of Analysis, Issue 24/4, 2017, Page(s) 445-476, ISSN 1073-2772
Publisher: International Press
DOI: 10.4310/MAA.2017.v24.n4.a2

The obstacle problem for the fractional Laplacian with critical drift

Author(s): Xavier Fernández-Real, Xavier Ros-Oton
Published in: Mathematische Annalen, Issue 371/3-4, 2018, Page(s) 1683-1735, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-017-1600-9

Regularity theory for general stable operators: Parabolic equations

Author(s): Xavier Fernández-Real, Xavier Ros-Oton
Published in: Journal of Functional Analysis, Issue 272/10, 2017, Page(s) 4165-4221, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2017.02.015

The Lagrangian Structure of the Vlasov–Poisson System in Domains with Specular Reflection

Author(s): Xavier Fernández-Real
Published in: Communications in Mathematical Physics, Issue 364/3, 2018, Page(s) 1327-1406, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-018-3242-5

Quantitative stability of the free boundary in the obstacle problem

Author(s): Sylvia Serfaty, Joaquim Serra
Published in: Analysis & PDE, Issue 11/7, 2018, Page(s) 1803-1839, ISSN 2157-5045
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/apde.2018.11.1803

On global solutions to semilinear elliptic equations related to the one-phase free boundary problem

Author(s): Xavier Fernández-Real, Xavier Ros-Oton
Published in: Discrete & Continuous Dynamical Systems - A, Issue 0/0, 2019, Page(s) 1-15, ISSN 1553-5231
Publisher: AIMS
DOI: 10.3934/dcds.2019238

Regularity of monotone transport maps between unbounded domains

Author(s): Dario Cordero-Erausquin, Alessio Figalli
Published in: Discrete & Continuous Dynamical Systems - A, Issue 39/12, 2019, Page(s) 7101-7112, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019297

On the optimal map in the $ 2 $-dimensional random matching problem

Author(s): Luigi Ambrosio, Federico Glaudo, Dario Trevisan
Published in: Discrete & Continuous Dynamical Systems - A, Issue 39/12, 2019, Page(s) 7291-7308, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019304

On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles

Author(s): Aleksei Kulikov, Lucas Oliveira, João P. G. Ramos
Published in: Revista Matemática Iberoamericana, 2022, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid

On the prescribed negative Gauss curvature problem for graphs

Author(s): Figalli, Alessio; Kehle, Christoph
Published in: Discrete and Continuous Dynamical Systems, 43 (3-4), Issue 29, 2023, ISSN 1531-3492
Publisher: American Institute of Mathematical Sciences
DOI: 10.48550/arxiv.2209.02326

Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

Author(s): Alessio Figalli; Yi Ru‐Ya Zhang
Published in: Communications on Pure and Applied Mathematics, Issue 1, 2021, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.22132

Perturbed Fourier uniqueness and interpolation results in higher dimensions

Author(s): João Pedro Ramos; Martin Stoller
Published in: Crossref, Issue 2, 2021, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2022.109448

The singular set in the Stefan problem

Author(s): Figalli, Alessio; Ros-Oton, Xavier; Serra, Joaquim
Published in: Journal of the American Mathematical Society, Issue 47, 2021, ISSN 0894-0347
Publisher: American Mathematical Society

A quantitative stability result for the Pr\'ekopa-Leindler inequality for arbitrary measurable functions

Author(s): Böröczky, Károly J.; Figalli, Alessio; Ramos, João P. G.
Published in: Ann. Inst. H. Poincaré Anal. Non Linéaire, Issue 5, 2022, ISSN 0294-1449
Publisher: Elsevier BV

Other (30)

Constraint maps with free boundaries: the obstacle case

Author(s): Figalli, Alessio; Kim, Sunghan; Shahgholian, Henrik
Published in: Issue 9, 2023
Publisher: arXiv

Infinite-width limit of deep linear neural networks

Author(s): Lénaïc Chizat, Maria Colombo, Xavier Fernández-Real, Alessio Figalli
Published in: 2022
Publisher: arXiv

A quantitative stability result for the sphere packing problem in dimensions 8 and 24

Author(s): Böröczky, Károly J.; Radchenko, Danylo; Ramos, João P. G.
Published in: Issue 5, 2023
Publisher: arXiv

A Faber-Krahn type inequality for log-subharmonic functions in the hyperbolic ball

Author(s): Kalaj, David; Ramos, João P. G.
Published in: Issue 14, 2023
Publisher: arXiv

The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains

Author(s): Matteo Bonforte, Alessio Figalli
Published in: 2023
Publisher: arXiv

Quantitative C1-stability of spheres in rank one symmetric spaces of non-compact type

Author(s): Lauro Silini
Published in: 2023
Publisher: arXiv

Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence

Author(s): Jean Dolbeault, Maria J. Esteban, Alessio Figalli, Rupert L. Frank, Michael Loss
Published in: 2022
Publisher: arXiv

Complete classification of global solutions to the obstacle problem

Author(s): Simon Eberle, Alessio Figalli, Georg S. Weiss
Published in: 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2208.03108

Regularity theory for nonlocal obstacle problems with critical and subcritical scaling

Author(s): Alessio Figalli, Xavier Ros-Oton, Joaquim Serra
Published in: 2023
Publisher: arXiv

The Multilinear Spherical Maximal Function in one dimension

Author(s): Georgios Dosidis, João P.G. Ramos
Published in: 2022
Publisher: arXiv

Stability of the Faber-Krahn inequality for the Short-time Fourier Transform

Author(s): Jaime Gómez, André Guerra, João P. G. Ramos, Paolo Tilli
Published in: 2023
Publisher: arXiv

Sharp Gaussian decay for the one-dimensional harmonic oscillator

Author(s): Danylo Radchenko, João P. G. Ramos
Published in: 2023
Publisher: arXiv

On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4+1

Author(s): Alessio Figalli, Joaquim Serra
Published in: 2019
Publisher: Analysis of PDEs

On the (In)stability of the Identity Map in Optimal Transportation

Author(s): Yash Jhaveri
Published in: 2019
Publisher: Analysis of PDEs

On the Continuity of Center-Outward Distribution and Quantile Functions

Author(s): Alessio Figalli
Published in: 2018
Publisher: Elsevier

On the fine structure of the free boundary for the classical obstacle problem

Author(s): Alessio Figalli, Joaquim Serra
Published in: 2019
Publisher: Springer

Regularity of interfaces in phase transitions via obstacle problems

Author(s): Alessio Figalli
Published in: 2018
Publisher: Analysis of PDEs

On the Monge-Ampère equation

Author(s): Alessio Figalli
Published in: 2019
Publisher: Analysis of PDEs

Free boundary regularity in obstacle problems

Author(s): Alessio Figalli
Published in: 2019
Publisher: Analysis of PDEs

A rigorous derivation from the kinetic Cucker-Smale model to the pressureless Euler system with nonlocal alignment

Author(s): Alessio Figalli, Moon-Jin Kang
Published in: 2019
Publisher: Mathematical Sciences Publishers

The Monge-Ampère Equation

Author(s): Connor Mooney
Published in: 2017
Publisher: European Mathematical Society

Singularities of complex-valued solutions to linear parabolic equations

Author(s): Connor Mooney
Published in: 2019
Publisher: Analysis of PDEs

REGULARITY RESULTS FOR THE EQUATION u11u22 = 1

Author(s): Connor Mooney, Ovidiu Savin
Published in: 2019
Publisher: Analysis of PDEs

On the singular set in the thin obstacle problem: higher order blow-ups and the very thin obstacle problem

Author(s): Xavier Fernández-Real, Yash Jhaveri
Published in: 2019
Publisher: Analysis of PDEs

Regularity of minimal surfaces with lower dimensional obstacles

Author(s): Xavier Fernánder-Real, Joaquim Serra
Published in: 2019
Publisher: Analysis of PDEs

Strong stability of convexity with respect to the perimeter

Author(s): Alessio Figalli, Yi Ru-Ya Zhang
Published in: 2023
Publisher: arXiv

Approaching the isoperimetric problem in ℂ via the hyperbolic log-convex density conjecture

Author(s): Lauro Silini
Published in: 2022
Publisher: arXiv

Effective dimension of machine learning models

Author(s): Amira Abbas, David Sutter, Alessio Figalli, Stefan Woerner
Published in: 2021
Publisher: arXiv

Expansion of the fundamental solution of a second-order elliptic operator with analytic coefficients

Author(s): Franceschini, Federico; Glaudo, Federico
Published in: Issue 38, 2021
Publisher: arXiv

C∞ partial regularity of the singular set in the obstacle problem

Author(s): Franceschini, Federico; Zatoń, Wiktoria
Published in: arXiv, Issue 36, 2021
Publisher: arXiv

Thesis and dissertations (1)

Regularity Results for Generated Jacobian Equations

Author(s): Jhaveri, Yash
Published in: Issue 3, 2018
Publisher: ETH Zurich
DOI: 10.3929/ethz-b-000274281