Aelson Sobral
- Postdoctoral Research Fellow, Applied Mathematics and Computational Sciences
Biography
Aelson Sobral is a postdoctoral researcher in the Free Boundary and Interface Problems group, led by Prof. Miguel Urbano at KAUST. He earned his PhD in Mathematics from the Federal University of Paraíba (UFPB), Brazil, before joining KAUST in September 2024. His research explores geometric frameworks to advance the regularity theory of fully nonlinear PDEs and Free Boundary Problems that are often born in phenomenon related to superconductivity and congested traffic dynamics.
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.
Education
- PhD (Dr. rer. nat.)
- Mathematics, Federal University of Paraíba, Brazil, 2024
Selected Publications
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.