Book

Peer-reviewed journal papers

  1. Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces (with G. Di Fazio and J.M. Urbano), submitted.
  2. Improved regularity for a nonlocal dead-core problem (with D. dos Prazeres and J.M. Urbano), submitted.
  3. Geometric properties of free boundaries in degenerate quenching problems (with D.J. Araújo and J.M. Urbano), submitted.
  4. A free boundary problem with fractional diffusion (with D. Marcon), submitted.
  5. The fractional Laplacian: a primer, Coimbra Mathematical Texts, Springer Cham, to appear.
  6. Interacting free boundaries in obstacle problems (with D.J. Araújo), Interfaces Free Bound. (2025).
  7. Fully nonlinear dead-core systems (with D.J. Araújo), J. Funct. Anal. 287 (2024), no. 9, Paper No. 110586, 23 pp.
  8. Sharp regularity for singular obstacle problems (with D.J. Araújo and V. Voskanyan), Math. Ann. 387 (2023), 1367-1401.
  9. An optimal Liouville theorem for the porous medium equation (with D.J. Araújo), Arch. Math. (Basel) 118 (2022), 427-433.
  10. Reaction-diffusion equations for the infinity Laplacian (with N. Diehl), Nonlinear Anal. 199 (2020), 111956, 12pp.
  11. Fully nonlinear integro-differential equations with deforming kernels (with L. Caffarelli and J.M. Urbano), Comm. Partial Differential Equations 45 (2020), 847-871.
  12. Singularly perturbed fully nonlinear parabolic equations and their asymptotic free boundaries (with G.C. Ricarte and J.M. Urbano), Rev. Mat. Iberoam. 35 (2019), 1535-1558.
  13. Sharp regularity estimates for quasilinear evolution equations (with M.D. Amaral, J.V. da Silva and G.C. Ricarte), Israel J. Math. 231 (2019), 25-45.
  14. Homogenization of obstacle problems in Orlicz-Sobolev spaces (with D. Marcon and J.F. Rodrigues), Port. Math. 75 (2018), 267-283.
  15. A free boundary optimization problem for the -Laplacian (with J.M. Urbano), J. Differential Equations 263 (2017), 1140-1159.
  16. Cavity type problems ruled by infinity Laplacian operator (with G.C. Ricarte and J.V. Silva), J. Differential Equations 262 (2017), 2135-2157.
  17. Optimal design problems with fractional diffusions (with E.V. Teixeira), J. Lond. Math. Soc. (2) 92 (2015), 338-352.
  18. On the regularity of the free boundary for quasilinear obstacle problems (with S. Challal, A. Lyaghfouri and J.F. Rodrigues), Interfaces Free Bound. 16 (2014), 359-394.
  19. On the two obstacles problem in Orlicz-Sobolev spaces and applications (with J.F. Rodrigues), Complex Var. Elliptic Equ. 56 (2011), 769-787.
  20. A one-phase parabolic problem with a free boundary in a convex ring (with M. Poghosyan), J. Contemp. Math. Anal. 44 (2009), 192-204.

    21. PhD thesis: Obstacle type problems in Orlicz-Sobolev spaces, University of Lisbon, UT Austin | Portugal CoLab program, 2013.