Xavier Ros-Oton

Universität Zürich

Institut für Mathematik, Y27 J20

Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

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

Curriculum Vitae

My research focuses on elliptic and parabolic Partial Differential Equations. I study:

• Free boundary problems

• Integro-differential equations

• Variational problems, stable solutions

• Fully nonlinear equations

• Evolution equations

• Isoperimetric inequalities

• Classical ODEs

For a brief description of these areas, see Research interests.

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.

  
  

  The results of this paper were announced in the Fields Medal Lecture of Alessio Figalli.

• 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

• Understanding singularities in free boundary problems, pdf

  Xavier Ros-Oton, Joaquim Serra,

  Matematica, Cultura e Societa (2019), to appear.

• 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.

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• http://user.math.uzh.ch/ros-oton/