Regularity and Stability in Partial Differential Equations

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

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

Regularity Results for Generated Jacobian Equations

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

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