Foto de Xavier Ros

Xavier Ros-Oton

Universität Zürich

Institut für Mathematik, Y27 J20

Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

email: xavier.ros-oton at math.uzh.ch


My research focuses on elliptic and parabolic Partial Differential Equations. I study:
For a brief description of these areas, see Research interests.

NEW: Postdoc position

A postdoctoral position is now open under my ERC Grant. The position will start in September 2019 (though it is quite flexible), and it is for 2 years.

Those wishing to apply are asked to send:
  • CV
  • Brief research statement (optional)
  • Between 1 and 3 recommendation letters (to be sent directly by the writers of the letters)
Applications will be considered on a continuing basis, with deadline December 1st, 2018.

Selected papers

For a complete list of all my articles and preprints (including some expository papers), see complete list of Publications.

  • On the singular set in the Stefan problem and a conjecture of Schaeffer,

    Alessio Figalli, Xavier Ros-Oton, Joaquim Serra,

    In preparation.

  • 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.

  • The structure of the free boundary in the fully nonlinear thin obstacle problem, pdf

    Xavier Ros-Oton, Joaquim Serra

    Adv. Math. 316 (2017), 710-747.

  • 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.

  • Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains, pdf

    Matteo Bonforte, Alessio Figalli, Xavier Ros-Oton,

    Comm. Pure Appl. Math. 70 (2017), 1472-1508.

  • Global regularity for the free boundary in the obstacle problem for the fractional Laplacian, pdf

    Begoña Barrios, Alessio Figalli, Xavier Ros-Oton,

    Amer. J. Math. 140 (2018), 415-447.

  • The Dirichlet problem for nonlocal operators with singular kernels: convex and nonconvex domains, pdf

    Xavier Ros-Oton, Enrico Valdinoci,

    Adv. Math. 288 (2016), 732-790.

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

    Xavier Ros-Oton, Joaquim Serra,

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

  • Sharp isoperimetric inequalities via the ABP method, pdf

    Xavier Cabré, Xavier Ros-Oton, Joaquim Serra,

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

  • The Pohozaev identity for the fractional Laplacian, pdf

    Xavier Ros-Oton, Joaquim Serra,

    Arch. Rat. Mech. Anal. 213 (2014), 587-628.

Some expository papers

  • Obstacle problems and free boundaries: an overview, pdf

    Xavier Ros-Oton,

    SeMA J. 75 (2018), 399-419.

  • Boundary regularity, Pohozaev identities, and nonexistence results, pdf

    Xavier Ros-Oton,

    Chapter 9 in the book Recent developments in Nonlocal Theory, De Gruyter, 2018.

  • Nonlocal elliptic equations in bounded domains: a survey, pdf

    Xavier Ros-Oton,

    Publ. Mat. 60 (2016), 3-26.

Awards

Collaborators

Theses

  • My PhD Thesis, defended on June 2014: pdf, slides

  • My Master's Thesis, defended on June 2011: pdf

For PhD students

- If you are interested on elliptic PDE:

- If you are interested on free boundary problems:

- If you are interested on integro-differential equations:

In Catalan/Spanish

  • Video of a talk given at the BBVA Foundation, aimed at the general public.
  • Video at the newspaper 'ABC.es'