Research
Publications
Book, scientific papers, doctoral thesis
Book
01
2025The fractional Laplacian uncovered
(with D. dos Prazeres and A. Sobral), 35° Colóq. Bras. Mat. 10, IMPA, Rio de Janeiro, 2025.Read publication
Scientific papers
23- 23Forthcoming
Sharp regularity for the anisotropic fractional Laplacian with Morrey data
(with J.M. Urbano), arXiv:2610.39947, submitted.Read publication - 22Forthcoming
Tumor growth models with nutrient consumption
(with D.J. Araújo and J.M. Urbano), arXiv:2610.37144, submitted.Read publication - 21
Forthcoming
Improved regularity for a nonlocal dead-core problem
(with D. dos Prazeres and J.M. Urbano), Indiana Univ. Math. J., to appear.Read publication - 202026
Geometric properties of free boundaries in degenerate quenching problems
(with D.J. Araújo and J.M. Urbano), SIAM J. Math. Anal. 58 (2026), 3599-3621.Read publication - 192026
Rectifiability of free boundaries in singular diffusion problems
Bull. Braz. Math. Soc. (N.S.) 57 (2026), 32.Read publication - 182026
Higher Hölder regularity for degenerate elliptic PDEs with data in Morrey spaces
(with G. Di Fazio and J.M. Urbano), Ann. Mat. Pura Appl. 205 (2026), 929-940.Read publication - 172026
Interacting free boundaries in obstacle problems
(with D.J. Araújo), Interfaces Free Bound. 28 (2026), 283-302.Read publication - 162026
Non-local diffusion with free boundaries
(with D. Marcon), J. Math. Anal. Appl. 555 (2026), 130183.Read publication - 15
- 142024
Fully nonlinear dead-core systems
(with D.J. Araújo), J. Funct. Anal. 287 (2024), no. 9, Paper No. 110586, 23 pp.Read publication - 132023
Sharp regularity for singular obstacle problems
(with D.J. Araújo and V. Voskanyan), Math. Ann. 387 (2023), 1367-1401.Read publication - 122022
An optimal Liouville theorem for the porous medium equation
(with D.J. Araújo), Arch. Math. (Basel) 118 (2022), 427-433.Read publication - 112020
Reaction-diffusion equations for the infinity Laplacian
(with N. Diehl), Nonlinear Anal. 199 (2020), 111956, 12pp.Read publication - 102020
Fully nonlinear integro-differential equations with deforming kernels
(with L. Caffarelli and J.M. Urbano), Comm. Partial Differential Equations 45 (2020), 847-871.Read publication - 092019
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.Read publication - 082019
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.Read publication - 072018
Homogenization of obstacle problems in Orlicz-Sobolev spaces
(with D. Marcon and J.F. Rodrigues), Port. Math. 75 (2018), 267-283.Read publication - 062017
A free boundary optimization problem for the ∞-Laplacian
(with J.M. Urbano), J. Differential Equations 263 (2017), 1140-1159.Read publication - 052017
Cavity type problems ruled by infinity Laplacian operator
(with G.C. Ricarte and J.V. Silva), J. Differential Equations 262 (2017), 2135-2157.Read publication - 042015
Optimal design problems with fractional diffusions
(with E.V. Teixeira), J. Lond. Math. Soc. (2) 92 (2015), 338-352.Read publication - 032014
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.Read publication - 022011
On the two obstacles problem in Orlicz-Sobolev spaces and applications
(with J.F. Rodrigues), Complex Var. Elliptic Equ. 56 (2011), 769-787.Read publication - 012009
A one-phase parabolic problem with a free boundary in a convex ring
(with M. Poghosyan), J. Contemp. Math. Anal. 44 (2009), 192-204.Read publication
Obstacle type problems in Orlicz-Sobolev spaces
University of Lisbon, UT Austin | Portugal CoLab program.
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