Publications and preprints

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

• X. Cabré, E. Cinti, J. Serra,
  Stable solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime,
  preprint arXiv:2111.06285

• A. Audrito, J. Serra,
  Interface regularity for semilinear one-phase problems,
  Adv. Math., accepted; preprint arXiv:2110.09210.

• 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,

• S. Dipierro, X. Ros-Oton, J. Serra, E. Valdinoci,
  Non-symmetric stable operators: regularity theory and integration by parts,
  Adv. Math. 401 (2022), Paper No. 108321.

• E. Cinti, F. Glaudo, A. Pratelli, X. Ros-Oton, J. Serra,
  Sharp quantitative stability for isoperimetric inequalities with homogeneous weights,
  Trans. Amer. Math. Soc. 375 (2022), 1509-1550.

• 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.

• X. Fernández-Real, J. Serra,
  Regularity of minimal surfaces with lower dimensional obstacles,
  J. Reine Angew. Math. 767 (2020), DOI: https://doi.org/10.1515/crelle-2019-0035.

• X. Cabré, E. Cinti, J. Serra,
  Stable $s$-minimal cones in $\mathbb R^3$ are flat for $s\sim 1$,
  J. Reine Angew. Math 764 (2020), DOI: https://doi.org/10.1515/crelle-2019-0005.

• 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.

• A. Figalli, J. Serra,
  On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1,
  IInvent. Math. 219 (2020), 153–177.

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

• X. Ros-Oton, J. Serra,
  The boundary Harnack principle for nonlocal elliptic equations in non-divergence form
  J. Potential Anal. 51 (2019), 51-315.

• X. Ros-Oton, J. Serra,
  The structure of the free boundary in the fully nonlinear thin obstacle problem,
  Adv. Math. 316 (2017), 710-747.

• 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 estimates for nonlocal elliptic equations in $C^1$ and $C^{1,\alpha}$ domains,
  Ann. Mat. Pura Appl. 196 (2017), 1637-1668.

• X. Cabré, J. Serra,
  An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions,
  Nonlinear Anal. Theor. 137 (2016), 246-265.

• X. Ros-Oton, J. Serra, E. Valdinoci,
  Pohozaev identities for anisotropic integro-differential operators,
  Comm. Partial Differential Equations 42 (2017), 1290-1321.

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

• X. Ros-Oton, J. Serra,
  Regularity theory for general stable operators,
  J. Differential Equations 260 (2016), 8675-8715.

• X. Ros-Oton, J. Serra,
  Local integration by parts and Pohozaev identities for higher order fractional Laplacians,
  Discrete Contin. Dyn. Syst. A 35 (2015), 2131-2150.

• 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.

• J. Serra,
  Regularity for fully nonlinear nonlocal parabolic equations with rough kernels,
  Calc. Var. Partial Differential Equations 54 (2015), 615-629.

• X. Ros-Oton, J. Serra,
  Nonexistence results for nonlocal equations with critical and supercritical nonlinearities,
  Comm. Partial Differential Equations 40 (2015), 115-133.

• X. Cabré, X. Ros-Oton, J. Serra,
  Sharp isoperimetric inequalities via the ABP method,
  J. Eur. Math. Soc. 18 (2016), 2971-2998.

• X. Ros-Oton, J. Serra,
  The extremal solution for the fractional Laplacian,
  Calc. Var. Partial Differential Equations 50 (2014), 723-750.

• X. Ros-Oton, J. Serra,
  The Pohozaev identity for the fractional Laplacian,
  Arch. Rational Mech. Anal. 213 (2014), 587-628.

• X. Ros-Oton, J. Serra,
  The Dirichlet problem for the fractional Laplacian: regularity up to the boundary,
  J. Math. Pures Appl. 101 (2014), 275-302.

• X. Cabré, X. Ros-Oton, J. Serra,
  Euclidean balls solve some isoperimetric problems with nonradial weights,
  C. R. Math. Acad. Sci. Paris 350 (2012), 945-947.

• X. Ros-Oton, J. Serra,
  Fractional Laplacian: Pohozaev identity and nonexistence results,
  C. R. Math. Acad. Sci. Paris 350 (2012), 505-508.

• J. Serra,
  Radial symmetry for diffusion equations with discontinuous nonlinearities,
  J. Differential Equations 254 (2013), 1893-1902.