Joaquim Serra

About me

I am currently SNF Ambizione Fellow at ETH Zurich (Switzerland).


My research is on elliptic and parabolic Partial Differential Equations.
The main research topics in which I have worked are:

  • Regularity of phase transitions (and its conection with minimal surface theory)
  • Free boundary regularity and study of singularities in the classical obstacle problem
  • Analysis of elliptic nonlinear integro-differential equations

Selected papers from the last 5 years (all of my papers are available at arXiv)

  • A. Figalli, X. Ros-Oton, J. Serra,
    Generic regularity of free boundaries for the obstacle problem,
    preprint arXiv:1912.00714.

  • X. Cabré, A. Figalli, X. Ros-Oton, J. Serra,
    Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
    Acta Math., to appear.

  • A. Figalli, J. Serra,
    On the fine structure of the free boundary for the classical obstacle problem,
    Invent. Math. 215 (2019), 311–366.

  • A. Figalli, J. Serra,
    On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1,
    Invent. Math., published online.

  • S. di Pierro, J. Serra, E. Valdinoci,
    Improvement of flatness for nonlocal phase transitions,
    Amer. J. Math, to appear.

  • E. Cinti, J. Serra, E. Valdinoci,
    Quantitative flatness results and BV-estimates for nonlocal minimal surfaces,
    J. Differential Geom. 112 (2019), 447-504.

  • L. Caffarelli, X. Ros-Oton, J. Serra,
    Obstacle problems for integro-differential operators: regularity of solutions and free boundaries,
    Invent. Math. 208 (2017), 1155-1211.

  • X. Ros-Oton, J. Serra,
    Boundary regularity for fully nonlinear integro- differential equations,
    Duke Math. J. 165 (2016), 2079-2154.