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.

Drop me a line if interested in a joint work:

Email: aelson[dot]sobral[at]kaust[dot]edu[dot]sa

I completed my PhD at the Federal University of Paraíba, Brazil, under the supervision of Professors Damião Araújo and Eduardo Teixeira. Prior to finishing my PhD, I spent a year as a research scholar with Professor Teixeira, focusing on regularity in Free Boundary Problems. Additionally, I had the opportunity to spend a few months at PUC-Rio, working with Professor Boyan Sirakov.

My research is the development of geometric tools for analyzing Free Boundary Problems.

You can find a more detailed CV here.

Back to Top

Research

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.

Papers

  • 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. Journal

  • D. dos Prazeres and A. Sobral Regularity estimates for nonlocal equations with an asymptotic property Partial Differ. Equ. Appl. 2 (2021), no. 3, Paper No. 33, 13 pp. Journal

    Preprints

  • D. Araújo, A. Sobral and E. Teixeira Regularity in diffusion models with gradient activation Submitted. arXiv

  • D. Araújo, A. Sobral, E. Teixeira and J. M. Urbano On free boundary problems shaped by oscillatory singularities Submitted. arXiv

  • T. Nascimento, G. Sá, A. Sobral and E. Teixeira Higher regularity of solutions to fully nonlinear elliptic equations Submitted. arXiv

  • A. Sobral, E. Teixeira, J.M. Urbano Degenerate free boundary problems with oscillatory singularities Submitted. arXiv

    • Back to Top