Currently, I am a Postdoctoral fellow at the Center for Mathematical Modeling (CMM), University of Chile, under the supervision of Prof. Gabrielle Nornberg.
Prior, I have held postdoctoral position at University of Central Florida under the supervision of Prof. Eduardo Teixeira and at State University of Campinas under the supervision of Prof. João Vitor da Silva.
I completed my Ph.D. graduation in January 2023 at the Federal University of Paraíba - Brazil, under the supervision of Professors Damião Araújo and Jose Miguel Urbano.
My research focuses on Partial Differential Equations (PDEs), with particular interest in regularity theory for free boundary problems involving elliptic and degenerate fully nonlinear operators.
Sharp regularity for a singular fully nonlinear parabolic free boundary problem
(with D. Araújo and J.M. Urbano) J. Differential Equations (2024)
Infinity Laplacian equations with singular absorptions
(with D. Araújo) Cal. of Var. and PDEs (2022) SBM Prize*
Comparison Principle, A.B.P.-type estimates for solutions of quasi-linear elliptic equations in non-divergence form and some implications
(with Jr. Bessa, R. Biswas, J. V. da Silva and M. Santos)
Regularity estimates for fully nonlinear dead-core problems with a Hamiltonian Term
(with R. Ramos)
Geometric regularity estimates for quasi-linear elliptic models in non-divergence form with strong absorption
(with C. Alcantara and J. V. da Silva)
Regularity estimates to quasi-linear parabolic equations in non-divergence form with non-homogeneous signature
(with Jr. Bessa and J. V. da Silva)
Improved regularity estimates for Hardy-Hénon-type equations driven by the ∞-Laplacian
(with E. Bezerra, J. V. da Silva and T Nascimento)
Sharp and improved regularity estimates for weighted quasilinear elliptic equations of p−Laplacian type and applications
(with J. V. da Silva, D. dos Prazeres and G. Ricarte).
Oscillatory free boundary problems in stochastic materials
(with D. Araújo, J. M. Urbano and E. Teixeira)
Higher regularity of solutions to fully nonlinear elliptic equations
(with A. Sobral, E. Teixeira and T. Nascimento)
Center for Mathematical Modeling (CMM)
Departamento de Ingeniería Matemática
Facultad de Ciencias Físicas y Matemáticas
Beauchef 851, Piso 4, office 415, Santiago, Chile.
gdesantana@dim.uchile.cl