My research interests are in Analysis and Partial Differential Equations (PDEs). I am particularly interested in regularity theory for fully nonlinear PDEs and their applications to free boundary problems and geometric analysis.
Publications:
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Schauder-type estimates for fully nonlinear degenerate elliptic equations. J. Funct. Anal. v. 289, no. 1 (2025), 110900.
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On the sharp Hessian integrability conjecture in the plane (with E. Texeira). J. Diff. Equations. 414 (2025), 890–903
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New regularity estimates for fully nonlinear elliptic equations ( with E. Teixeira). J. Math. Pures Appl. 171 (2023), 1-25.
Pre-prints:
Regularity of solutions to degenerate and singular free boundary problems with volume constraint. ( with H. X. Nguyen and P.R. Stinga). Submitted (2025)
Optimal regularity for degenerate elliptic equations with Hamiltonian terms. (with P. Andrade). Submitted (2025).
Interior regularity estimates for fully nonlinear equations with arbitrary nonhomogeneous degeneracy laws (with P. Andrade). Submitted (2025).
Improved regularity estimates for Hardy-Hénon-type equations driven by Infinity Laplacian. (with E.C. Bezerra Júnior, J.V. Da Silva, and G. Sá). Submitted (2024).
Higher regularity of solutions to fully nonlinear elliptic equations (with G. Sa, A. Sobral, and E. Teixeira). Submitted (2024)