Selected papers

  1. Complete classification of global solutions to the obstacle problem (with S. Eberle and G.S. Weiss)
  2. The singular set in the Stefan problem (with X. Ros-Oton and J. Serra)
  3. 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
  4. Sharp gradient stability for the Sobolev inequality (with Y. Ru-Ya Zhang)
    Duke Math. J., to appear
  5. 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.
  6. 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.
  7. 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.
  8. On the fine structure of the free boundary for the classical obstacle problem (with J. Serra)
    Invent. Math., 215 (2019), no. 1, 311-366.
  9. 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.
  10. Universality in several-matrix models via approximate transport maps (with A. Guionnet)
    Acta Math. 217 (2016), no. 1, 81-176.
  11. Partial regularity for optimal transport maps (with G. De Philippis)
    Publ. Math. Inst. Hautes Études Sci. 121 (2015), 81-112.
  12. Generic hyperbolicity of Aubry sets on surfaces (with G. Contreras and L. Rifford)
    Invent. Math. 200 (2015), no. 1, 201-261.
  13. 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.
  14. W2,1 regularity for solutions of the Monge-Ampère equation (with G. De Philippis)
    Invent. Math. 192 (2013), no. 1, 55-69.
  15. 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.
  16. A mass transportation approach to quantitative isoperimetric inequalities (with F. Maggi and A. Pratelli)
    Invent. Math. 182 (2010), no. 1, 167-211.