Selected papers

  1. Sharp stability for Sobolev and log-Sobolev inequalities, with optimal dimensional dependence (with J. Dolbeault, M. J. Esteban, R. L. Frank, M. Loss)
    Preprint
  2. Complete classification of global solutions to the obstacle problem (with S. Eberle and G.S. Weiss)
    Preprint
  3. The singular set in the Stefan problem (with X. Ros-Oton and J. Serra)
    Preprint
  4. Strong Sard Conjecture and regularity of singular minimizing geodesics for analytic sub-Riemannian structures in dimension 3 (with A. Belotto da Silva, A. Parusiński and L. Rifford)
    Invent. Math., to appear
  5. Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)
    Duke Math. J., to appear
  6. Generic regularity of free boundaries for the obstacle problem (with X. Ros-Oton and J. Serra)
    Publ. Math. Inst. Hautes Études Sci. 132 (2020), 181–292.
  7. Stable solutions to semilinear elliptic equations are smooth up to dimension 9 (with X. Cabré, X. Ros-Oton and J. Serra)
    Acta Math. 224 (2020), no. 2, 187–252.
  8. On stable solutions for boundary reactions: a De Giorgi type result in dimension 4+1 (with J. Serra)
    Invent. Math., 219 (2020), no. 1, 153-177.
  9. On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
    Invent. Math., 215 (2019), no. 1, 311-366.
  10. On the Lagrangian structure of transport equations: the Vlasov-Poisson system (with L. Ambrosio and M. Colombo)
    Duke Math. J. 166 (2017), no. 18, 3505-3568.
  11. Universality in several-matrix models via approximate transport maps (with A. Guionnet)
    Acta Math. 217 (2016), no. 1, 81-176.
  12. Partial regularity for optimal transport maps (with G. De Philippis)
    Publ. Math. Inst. Hautes Études Sci. 121 (2015), 81-112.
  13. Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)
    Invent. Math. 200 (2015), no. 1, 201-261.
  14. Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation (with E. Carlen)
    Duke Math. J. 162 (2013), no. 3, 579-625.
  15. W2,1 regularity for solutions of the Monge-Ampère equation (with G. De Philippis)
    Invent. Math. 192 (2013), no. 1, 55-69.
  16. Global in time measure-valued solutions and finite-time aggregation for nonlocal interaction equations (with J. A. Carrillo, M. Di Francesco, T. Laurent, and D. Slepcev)
    Duke Math. J. 156 (2011), no. 2, 229-271.
  17. A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
    Invent. Math. 182 (2010), no. 1, 167-211.