Joaquim Serra

About me

I am currently Assistant Professor of Mathematics at ETH Zurich.


My research is on Elliptic Partial Differential Equations.
More precisely:

  • Stable interfaces (phase transitions and minimal surfaces)
  • Free boundaries (the singular sets in the obstacle problem and the Stefan problem)
  • Elliptic and parabolic integro-differential equations (integration by part type identities with singular boundary terms, regularity for fully nonlinear equations)
  • Reaction-diffusion equations, isoperimetric problems

Selected papers from the last 5 years
(all of my papers are available at arXiv; see also the Publications page for direct links to pdf).

  • F. Franceschini, J. Serra,
    Free boundary partial regularity in the thin obstacle problem,
    preprint arXiv:2112.11104.

  • A. Figalli, X. Ros-Oton, J. Serra,
    The singular set in the Stefan problem,
    preprint arXiv:2103.13379.
    See also M. Rovrig's story in Quanta Magazine: Mathematicians Prove Melting Ice Stays Smooth,

  • A. Figalli, X. Ros-Oton, J. Serra,
    Generic regularity of free boundaries for the obstacle problem,
    Publ. Math. IHÉS 159 (2020), 181-292.

  • X. Cabré, A. Figalli, X. Ros-Oton, J. Serra,
    Stable solutions to semilinear elliptic equations are smooth up to dimension 9,
    Acta Math., 224 (2020), 187-252.

  • 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. 219 (2020), 153–177.

  • 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.