Associate Professor
Department of Mathematics
Universidade Federal da Paraíba · UFPB
araujo@mat.ufpb.br
I am currently based in the vibrant city of João Pessoa, state of Paraíba, Brazil, in the Department of Mathematics at the Universidade Federal da Paraíba. I am conducting research into geometric and analytical techniques for partial differential equations and free boundary problems. Our aim is to provide precise regularity (smoothness) estimates of solutions to these problems. Regularity is crucial for numerical computations, and a lack of smoothness can describe how wild the behavior of models are. Of particular interest are my recent works on problems involving degenerate PDEs, in which the diffusion properties of governing operators degenerate along free boundaries - a priori unknown sets. One notable example is the phenomenon of ice melting into water, where the free boundary refers to the interface between water and ice, namely, the solid-liquid interface. Such mathematical scenarios are also related to jet and cavitational flows, gas and liquid flows in porous media, and financial mathematics, among others.
These lecture notes serve as an introduction to the analysis of 1harmonic functions, a subject that has significantly matured in recent years within the field of nonlinear partial differential equations. They are based on the minicourses we taught online during the pandemic at the Universidade Federal da Paraíba (João Pessoa, Brazil) and at the 24th Brazilian Mathematical Colloquium in IMPA (Rio de Janeiro, Brazil) in July 2023. Shorter versions of these lectures were previously delivered by the second author at the Universidade Federal do Ceará (Fortaleza, Brazil) in the (southern hemisphere) Summer of 2013, at Aalto University (Helsinki, Finland) in the (northern hemisphere) Spring of 2013 and at KAUST (Thuwal, Saudi Arabia) early in 2017, and by the first author at the Universidade Federal do Rio de Janeiro (Rio de Janeiro, Brazil) in the (southern hemisphere) Summer of 2020
We warmly invite students of all levels and disciplines related to mathematics to reach out to us regarding research projects centered around introductory topics in the analysis of differential equations, functional analysis, and measure theory, whether you are an undergraduate, master's, or Ph.D. We strongly encourage girls to join our research group, as we are committed to promoting inclusivity and gender equality in scientific research.
Diego dos Santos, Ph.D. student
Aureliana Tavares, M.S. student
Renato de Andrade, Undergrad student
Felipe de Andrade, Undergrad student
Lucas Pontes, Undergrad student
José Ygor Leal, Highschool student
Marlisson dos Santos, Highschool student
Aelson Sobral, Ph.D. student | 2024
Co-advised by Eduardo Teixeira (University of Central Florida - USA)
Thesis Publications: To appear
Current Position: Post-Doctorate Fellow at KAUST - Saudi Arabia
Ginaldo S. Sá, Ph.D. student | 2023
Co-advised by José Miguel Urbano (KAUST - Saudi Arabia)
Thesis: J. Differential Equations & Calc. Var. Partial Differential Equations (awarded SBM Prize, 2023)
Current Position: Post-Doctorate Fellow at the University of Central Florida
Harish Shrivastava, Post-Doctorate | 2019
INCTMat CNPq fellowship