Aelson Sobral
- Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences
Aelson Sobral's research focuses on developing geometric frameworks to address the regularity theory of fully nonlinear PDEs and Free Boundary Problems arising from superconductivity and congested traffic dynamics.
Biography
Aelson Sobral earned his PhD in March 2024 from the Federal University of Paraíba (UFPB), Brazil. He subsequently spent six months as a visiting researcher at the Pontifical Catholic University of Rio de Janeiro and joined KAUST in September 2024.
Research Interests
Aelson Sobral's research centers on developing geometric tools to analyze Free Boundary Problems, focusing on regularity theory for degenerate and singular partial differential equations (PDEs) and free boundary regularity. These problems are intrinsically linked to flame propagation and congested traffic dynamics.
About
Selected publications
D.. dos Prazeres, A. Sobral and J.M. Urbano, Cordes-Nirenberg type results for nonlocal equations with deforming kernels, J. Funct. Anal. 287 (2024), no. 9, Paper No. 110593, 33 pp.
Recent preprints
- D. Araújo, A. Sobral and E. Teixeira, Regularity in diffusion models with gradient activation, arxiv.
- D. Araújo, A. Sobral, E. Teixeira and J. M. Urbano, On free boundary problems shaped by oscillatory singularities,
arxiv - T. Nascimento, G. Sá, A. Sobral and E. Teixeira, Higher regularity of solutions to fully nonlinear elliptic equations,
arxiv - A. Sobral, E. Teixeira, and J.M. Urbano, Degenerate free boundary problems with oscillatory singularities.
Education
- PhD (Dr. rer. nat.)
- Mathematics, Federal University of Paraíba, Brazil, 2024