Dr. Joaquim Serra

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.