About me

Associate Professor of Mathematics at ETH Zurich; CV

Research area: Elliptic Partial Differential Equations and related topics.

Selected papers (Find here a full publication list and here all my papers in arXiv)

• E. Florit-Simon, J. Serra,
  On stable solutions to the Allen–Cahn equation with bounded energy density in $\mathbb{R}^4$,
  preprint arXiv:2509.02739.

• H. Chan, X. Fernández-Real, A. Figalli, J. Serra,
  Global stable solutions to the free boundary Allen–Cahn and Bernoulli problems in 3D are one-dimensional,
  J. Amer. Math. Soc., accepted.

• M. Caselli, E. Florit, J. Serra,
  Yau's conjecture for nonlocal minimal surfaces,
  J. Eur. Math. Soc., accepted.

• H. Chan, S. Dipierro, E. Valdinoci, J. Serra,
  Nonlocal approximation of minimal surfaces: optimal estimates from stability,
  Comm. Pure. Appl. Math., accepted.

• F. Franceschini, J. Serra,
  Free boundary partial regularity in the thin obstacle problem,
  Comm. Pure. Appl. Math. 77 (2024), 630-669.

• A. Figalli, X. Ros-Oton, J. Serra,
  The singular set in the Stefan problem,
  J. Amer. Math. Soc. 37 (2024), 305-389,
  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 142 (2020), 1083-1160.

• 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.