Xavier Ros-Oton

Full professor at UB
Research area: Partial Differential Equations

PhD in Mathematics obtained at Universitat Politècnica de Catalunya


Xavier Ros-Oton is an ICREA Research Professor at the University of Barcelona since 2020. Previously, he has been Assistant Professor at Universität Zürich, as well as R. H. Bing Instructor at the University of Texas at Austin.

He is a mathematician who works on Partial Differential Equations (PDEs). Specifically, he studies the regularity of solutions to elliptic and parabolic PDEs, and he is mostly known for his results on free boundary problems and integro-differential equations.

He is the PI of an ERC Starting Grant (2019-2024), and has received several awards for young mathematicians in Spain, including the J. L. Rubio de Francia Prize from the RSME and the Antonio Valle Prize from the SeMA.

In 2019, he received the Scientific Research Award from the Fundación Princesa de Girona.

Research lines

  • Free boundary problems
  • Integro-differential equations
  • Variational problems, stable solutions
  • Fully nonlinear equations
  • Evolution equations
  • Isoperimetric inequalities

Selected publications

Generic regularity of free boundaries for the obstacle problem,

Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,

Publ. Math. IHÉS, in press (2020).


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

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

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


Free boundary regularity in the parabolic fractional obstacle problem,

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,

Luis Caffarelli, Xavier Ros-Oton, Joaquim Serra

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


Boundary regularity for fully nonlinear integro-differential equations,

Xavier Ros-Oton, Joaquim Serra,

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


Link to Google Schoolar:  https://scholar.google.com/citations?user=vzEtYagAAAAJ

Link to ArXiv:  https://arxiv.org/search/math?searchtype=author&query=Ros-Oton%2C+X