I am a Postdoctorate fellow in the Computer, Electrical and Mathematical Sciences and Engineering Division (CEMSE) at King Abdullah University of Science and Technology (KAUST) in Saudi Arabia.
I completed my PhD at the Federal University of Paraíba (Brazil), advised by Professors Damião Araújo and Eduardo Teixeira. Before graduating, I spent a year as a research scholar with Professor Teixeira at the University of Central Florida. After graduation, and before moving to Saudi Arabia, I undertook a research stay at PUC-Rio with Professor Boyan Sirakov.
My research focuses on developing geometric tools to analyze Free Boundary Problems, with a particular interest in regularity theory for degenerate and singular PDEs, as well as free boundary regularity. Recently, I’ve also become interested in generalized maximum principles for elliptic equations in both divergence and non-divergence forms.
You can find a more detailed CV here.
Back to TopPublications
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On a nonlocal superconductivity problem.
To appear in Rev. Mat. Iberoamericana (2026) · D. Araújo and A. Sobral
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On free boundary problems shaped by varying singularities
Calc. Var. PDE (2026) · D. Araújo, A. Sobral, E. Teixeira, and J. M. Urbano
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Regularity in diffusion models with gradient activation
J. Funct. Anal. (2025) · D. Araújo, A. Sobral and E. Teixeira
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Degenerate free boundary problems with oscillatory singularities
Partial Differ. Equ. Appl. (2025) · A. Sobral, E. Teixeira and J.M. Urbano
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Cordes-Nirenberg type results for nonlocal equations with deforming kernels
J. Funct. Anal. (2024) · D. dos Prazeres, A. Sobral and J. M. Urbano
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Regularity estimates for nonlocal equations with an asymptotic property
Partial Differ. Equ. Appl. (2021) · D. dos Prazeres and A. Sobral
Preprints
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Aleksandrov-Bakelman-Pucci estimates for degenerate parabolic equations and applications.
Submitted (2026) · F. Charro and A. Sobral
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On Weiss Almost Monotonicity Formula.
Submitted (2026) · A. Sobral
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Fractional p-caloric functions are Lipschitz.
Submitted (2026) · D. Jesus, A. Sobral and J. M. Urbano
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On the regularity of minimizers arising from singular minimal surface-like energies.
Submitted (2025) · A. Sobral, E. Teixeira and J. M. Urbano
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Keller-Osserman and Harnack type results for nonlinear elliptic PDE with unbounded ingredients.
Submitted (2025) · B. Sirakov and A. Sobral
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Regularity estimates for PDEs with nonlocal degeneracies.
Submitted (2025) · D. Araújo, A. Sobral, E. Teixeira and J. M. Urbano
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Borderline regularity in singular free boundary problems.
Submitted (2025) · D. Araújo, A. Sobral, E. Teixeira and J. M. Urbano
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Higher regularity of solutions to fully nonlinear elliptic equations
Submitted (2024) · T. Nascimento, G. Sá, A. Sobral and E. Teixeira