Xavier Ros Oton

Kinetic equations

• Optimal regularity for kinetic Fokker-Planck equations in domains, pdf

  Xavier Ros-Oton, Marvin Weidner,

  preprint arXiv (2025).

• Regularity for the Boltzmann equation conditional to pressure and moment bounds, pdf

  Xavier Fernandez-Real, Xavier Ros-Oton, Marvin Weidner,

  Comm. Math. Phys. 406 (2025), 175.

Free boundary problems

• Optimal regularity for the fully nonlinear thin obstacle problem, pdf

  Maria Colombo, Xavier Fernandez-Real, Xavier Ros-Oton,

  J. Eur. Math. Soc. 27 (2025), 3793-3840.

• The singular set in the Stefan problem, pdf

  Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,

  J. Amer. Math. Soc. 37 (2024), 305-389.

Quanta Magazine: 'Mathematicians Prove Melting Ice Stays Smooth'

• Generic regularity of free boundaries for the obstacle problem, pdf

  Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,

  Publ. Math. Inst. Hautes Études Sci. 132 (2020), 181-292.

Other elliptic/parabolic PDE

• Optimal regularity and fine asymptotics for the porous medium equation in bounded domains, pdf

  Tianling Jin, Xavier Ros-Oton, Jingang Xiong,

  J. Reine Angew. Math. 809 (2024), 269-300.

• Stable solutions to semilinear elliptic equations are smooth up to dimension 9, pdf

  Xavier Cabré, Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,

  Acta Math. 224 (2020), 187-252.

• Sharp isoperimetric inequalities via the ABP method, pdf

  Xavier Cabré, Xavier Ros-Oton, Joaquim Serra,

  J. Eur. Math. Soc. 18 (2016), 2971-2998.

Nonlocal free boundary problems

• Optimal regularity for supercritical parabolic obstacle problems, pdf

  Xavier Ros-Oton, Clara Torres-Latorre,

  Comm. Pure Appl. Math. 77 (2024), 1724-1765.

• Free boundary regularity in the parabolic fractional obstacle problem, pdf

  Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,

  Comm. Pure Appl. Math. 71 (2018), 2129-2159.

• Obstacle problems for integro-differential operators: regularity of solutions and free boundaries, pdf

  Luis Caffarelli, Xavier Ros-Oton, Joaquim Serra

  Invent. Math. 208 (2017), 1155-1211.

Nonlocal equations

• The fractional Laplacian in Lipschitz domains: Dahlberg theorem and L^2 solvability,

  Roberto Colombo, Xavier Fernandez-Real, Xavier Ros-Oton,

  forthcoming.

• Semiconvexity estimates for nonlinear integro-differential equations, pdf

  Xavier Ros-Oton, Clara Torres-Latorre, Marvin Weidner,

  Comm. Pure Appl. Math. 78 (2025), 592-647.

• Boundary regularity for fully nonlinear integro-differential equations, pdf

  Xavier Ros-Oton, Joaquim Serra,

  Duke Math. J. 165 (2016), 2079-2154.

Boards and Committees

• Editorial Board member of Analysis & PDE (2025 - present).

• Editorial Board member of Rev. Mat. Iberoam. (2024 - 2026).

• Editorial Board member of Calc. Var. PDE (2020 - 2023).

• Editorial Board member of Nonlinear Analysis (2020 - 2023).

• Editorial Board member of Disc. Cont. Dyn. Syst. A (2023 - 2025).

• Editorial Board member of Collectanea Mathematica (2021 - 2025).

• Scientific Committee member of Rev. Acad. Cienc. Ser. A Math. (2022 - present).

• President of the committee of the Catalan Mathematical Olympiad (2020 - present).

Awards

• Highly Cited Researcher 2025

  The list is based on citation data (and other metrics) over the past 11 years. Only 65 mathematicians were selected.

• Premi Nacional de Recerca al Talent Jove 2024

  Awarded annually to a researcher under 40 years, working in any area of knowledge. First mathematician to receive the award.

  This is the most important prize for young researchers in Catalunya.

• PI of the ERC Consolidator Grant   'SSNSD'   (2024 - 2029)

  Awarded amount: 1,682,500€

• Premio Nacional de Investigación para Jóvenes 2023 en Matemáticas y Tecnologías de la Información y las Comunicaciones

  Awarded annually to a Spanish mathematician or computer scientist under 40 years. First mathematician to receive the award.

  The prize, given by the Spanish Government, comes with a monetary award of 30,000€.

• Frontiers of Science Awards 2023

  International prize given to 86 papers in all areas of Mathematics published in 2018--2022.

  Awarded twice for the articles "Generic regularity of free boundaries for the obstacle problem"

  and "Stable solutions to semilinear elliptic equations are smooth up to dimension 9".

  The prize is given by the government of China at the International Congress of Basic Science.

• Ferran Sunyer i Balaguer Prize 2023

  Awarded for the book "Integro-Differential Elliptic Equations", with X. Fernandez-Real.

  The Prize comes with a monetary award of 15,000€.

• Académico Correspondiente of the Spanish Royal Academy of Sciences

  Elected on October 2022. Youngest member of the Academy.

• Stampacchia Gold Medal 2021

  International prize awarded every three years in recognition of outstanding contributions to the Calculus of Variations.

  The medal, named after Guido Stampacchia, goes to a mathematician whose age does not exceed 35.

• Premio FPdGi Investigación Científica 2019 from the Fundación Princesa de Girona

  Awarded anually to a young Spanish scientist under 35 years.

  The prize is given by the King of Spain, and comes with a monetary award of 20,000€.

• PI of the ERC Starting Grant   'EllipticPDE'   (2019 - 2024)

  Awarded amount: 1,335,250€

  Youngest awardee of ERC Starting Grant 2018 (among all panels in all sciences)

• PI of SNSF Research Project (2018 - 2020)

  Awarded amount: 200,000CHF

• Premio Antonio Valle 2017 from the Spanish Society of Applied Mathematics

  Award to the best researcher under 34 years. At age 29, I became the youngest winner of the award ever.

• Premio Jose Luis Rubio de Francia 2017 from the Real Sociedad Matemática Española

  Awarded anually to a young mathematician from Spain or residing in Spain.

  It is the highest distinction given by the RSME, and one of the most important prizes in Mathematics in Spain.

• PI of the NSF Analysis Grant DMS-1565186 (2016 - 2017)

  Awarded amount: $103,617

• Premio Vicent Caselles 2015 from the Real Sociedad Matemática Española

  Spanish award to the best PhD theses in Mathematics

• Extraordinary PhD Prize from the Universitat Politecnica de Catalunya

• Premi Évariste Galois 2012 from the Societat Catalana de Matemàtiques

• Bronze Medal at the International Mathematical Olympiad 2006