Xavier 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), has received several awards for young mathematicians in Spain, as well as the Scientific Research Award from the Fundación Princesa de Girona in 2019. Furthermore, in 2021 he was awarded the Stampacchia Gold Medal, an international prize awarded every three years in recognition of outstanding contributions to the Calculus of Variations.
Personal webpage: https://www.ub.edu/pde/xros
- Elliptic and parabolic PDE.
- Free boundary problems
- Calculus of Variations
ERC Starting Grant 'EllipticPDE' (2019-2024). Budget: 1,335,000€
Generic regularity of free boundaries for the obstacle problem,
Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,
Publ. Math. IHÉS 132 (2020), 181-292.
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.