Elliptic PDEs

Published/accepted papers

  1. 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.
  2. 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.
  3. Optimal regularity for the convex envelope and semiconvex functions related to supersolutions of fully nonlinear elliptic equations (with J. E. M. Braga and D. Moreira)
    Comm. Math. Phys., 367 (2019), no. 1, 1-32.
  4. Optimal regularity of the convex envelope (with G. De Philippis)
    Trans. Amer. Math. Soc. 367 (2015), no. 6, 4407-4422.
  5. An excess-decay result for a class of degenerate elliptic equations (with M. Colombo)
    Discrete Contin. Dyn. Syst. Ser. S 7 (2014), no. 4, 631-652.
  6. Regularity results for very degenerate elliptic equations (with M. Colombo)
    J. Math. Pures Appl. (9) 101 (2014), no. 1, 94-117.

Submitted papers

  1. Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations (with Y. Ru-Ya Zhang)