Damião Júnio Araújo


Associate Professor
Department of Mathematics
Universidade Federal da Paraíba · UFPB
araujo@mat.ufpb.br

Interests


I am currently based in João Pessoa - Paraíba - Brazil, in the Department of Mathematics at UFPB. My research interests include Partial Differential Equations, Calculus of Variations and Geometric Analysis. I have also been engaged in applications of regularity theory for non-linear diffusive processes and free boundary problems arising from geometry, thermodynamics, fluid dynamics, material sciences, financial engineering, among others. Of particular interest are my recent works on degenerate PDEs, which comprise systems in which the diffusion properties of governing operators degenerate along a priori unknown sets.

Published and Accepted papers


  • On a two-phase free boundary problem ruled by the infinity Laplacian. (with E. Teixeira and J.M. Urbano)
    Israel Journal of Math., to appear.

  • Higher regularity estimates for the porous medium equation near the heat equation.
    Rev. Mat. Iberoam. 37 (2021), 1747-1760.

  • Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian. (with L. Mari and L. Pessoa)
    J. Differential Equations, Volume 281, 25 April 2021, Pages 550--587.

  • Optimal C^{1,\alpha} estimates for a class of elliptic quasilinear equations. (with L. Zhang)
    Commun. Contemp. Math. 22 (2020), no. 5, 1950014, 19 pp.

  • Sharp regularity for the inhomogeneous porous medium equation. (with A. Maia and J.M. Urbano)
    Journal d'Analyse Mathématique, J. Anal. Math. 140 (2020), 395-407.

  • Towards the C^{p'} -regularity conjecture in higher dimensions. (with E. Teixeira and J.M. Urbano)
    Int Math Res Notices, Volume 2018, Issue 20, 2018, P. 6481-6495.

  • A proof of the C^{p'}-regularity conjecture in the plane. (with E. Teixeira and J.M. Urbano)
    Adv. Math. 316, 541–553, (2017).

  • Singularly pertubed equations of degenerate type. (with E. Teixeira and G. Ricarte)
    Ann. Inst. H. Poincaré Anal. Non linéaire 34, no. 3, 655-678,(2017).

  • Infinity Laplacian equation with strong absorptions. (with E. Teixeira and R. Leitão)
    J. Funct. Analysis 270, pp.2249-2267, (2016).

  • Geometric gradient estimates for solutions to degenerate elliptic equations. (with E. Teixeira and G. Ricarte)
    Cal. of Var. and PDEs, Vol.53, Issue 3-4, pp 605-625, (2015).

  • Geometric approach nonvariational singular elliptic equations. (with E. Teixeira)
    Arc. for Rat. Mech. and Anal., Vol.209, Issue 3, pp 1019-1054, (2013).

Submitted papers



  • Fully nonlinear dead-core systems.
    (with R. Teymurazyan)

  • Infinity Laplacian equations with singular absorptions.
    (with Ginaldo Sá)

  • Improved boundary and global regularity for degenerate fully nonlinear elliptic equations.
    (with B. Sirakov)

  • An optimal Liouville theorem for the porous medium equation.
    (with R. Teymurazyan)

CV and others




Currículo Lattes (In Portuguese)

Teamwork



Ginaldo S. Sá , Ph.D. student
Aelson O. Sobral , Ph.D. student
Rafael Costa , M.S. student
Renan Santos , Undergrad student
Renato de Andrade , Undergrad student
Hendric Miguel Amaral , Highschool student


Past

Harish Shrivastava , Post-Doctorate | 2019-2020