About me

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

Full Curriculum Vitae

My research is on elliptic and parabolic Partial Differential Equations.
See below the main research topics in which I have worked, with selected publications for each of them.

• Free boundary regularity and singularities in the classical obstacle problem

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

  • S. Serfaty, J. Serra,
    Quantitative stability of the free boundary in the obstacle problem,
    Anal. PDE 11 (2018), 1803–1839.

• Regularity of phase transitions (in connection with minimal surfaces)

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

  • 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. Diff. Geom, to appear.

• Analysis of elliptic nonlinear integro-differential equations

  • 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.

  • J. Serra,
    $C^{\sigma+\alpha}$ regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels,
    Calc. Var. Partial Differential Equations 54 (2015), 3571-3601.