Research

RESEARCH INTERESTS


PAPERS

15. Nornberg, Gabrielle; Prazeres, Disson dos; Quaas, Alexander. Fundamental solutions and critical Lane-Emden exponents for nonlinear integral operators in cones, Journal of Functional Analysis v. 287, Issue 4, 2024. (link, arXiv) 

14. Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. Classification of radial solutions for fully nonlinear equations with Hardy potential. Discrete and Continuous Dynamical Systems, v. 44, Issue 8, p.2232-2251. 2024. (link)

13. Maia, Liliane; Moreira dos Santos, Ederson; Nornberg, Gabrielle. Radial solvability for Pucci-Lane-Emden systems in annuli. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, v. 154, Issue 2, p. 494-507, 2024. (link)

12. Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. Existence, nonexistence and uniqueness for Lane-Emden type fully nonlinear systems. Nonlinearity 36, no. 3, p. 1510–1546, 2023. (link, arXiv)

11. Moreira dos Santos, Ederson; Nornberg, Gabrielle; Schiera, Delia; Tavares, Hugo. Principal spectral curves for Lane-Emden fully nonlinear type systems and applications. Calculus of Variations and Partial Differential Equations 62 (2023), no. 2, Paper No. 49, 38 pp. (link, arXiv)

10. Maia, Liliane; Nornberg, Gabrielle. Radial solutions for Hénon type fully nonlinear equations in annuli and exterior domains. Mathematics in Engineering, v. 4, Issue 6, p. 1-18, 2022. (link, arXiv)

9. da Silva, João Vitor; Nornberg, Gabrielle. Regularity estimates for fully nonlinear elliptic PDEs with general Hamiltonian terms and unbounded ingredients. Calculus of Variations and Partial Differential Equations v. 60, n. 202, 2021. (link, arXiv)

8. Moreira dos Santos, Ederson; Nornberg, Gabrielle; Soave, Nicola . On unique continuation principles for some elliptic systems. Annales de l'Institut Henri Poincaré Analyse Non Linéaire, v.38, Issue 5, p. 1667-1680,  2021. (link, arXiv, talk)

7. Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. A dynamical system approach to a class of radial weighted fully nonlinear equations. Communications in Partial Differential Equations, v.46, Issue 4, p. 573-610, 2021. (link, arXiv)

6. Moreira dos Santos, Ederson; Nornberg, Gabrielle. Symmetry properties of positive solutions for fully nonlinear elliptic systems. Journal of Differential Equations, v. 269, Issue 5, p. 4175-4191, 2020. (link, arXiv)

5. Nornberg, Gabrielle; Schiera, Delia; Sirakov, Boyan. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete and Continuous Dynamical Systems, s. A, v. 40, n. 6, p. 3857-3881, 2020. (link, arXiv)

4. Nornberg, Gabrielle. C1,α regularity for fully nonlinear elliptic equations with superlinear growth in the gradient. Journal de Mathématiques Pures et Appliquées, v. 128, p. 297-329, 2019. (link, arXiv)

3. Nornberg, Gabrielle; Sirakov, Boyan . A priori bounds and multiplicity for fully nonlinear equations with quadratic growth in the gradient. Journal of Functional Analysis, v. 276, p. 1806-1852, 2019. (link, arXiv)

2. Bourchtein, Ludmila; Bourchtein, Andrei; Nornberg, Gabrielle; Venzke, Cristiane. A Hierarchy of the Convergence Tests Related to Cauchy's Test. Int. Journal of Mathematical Analysis, v. 6, p. 1847-1869, 2012. (link)

1. Bourchtein, Ludmila; Bourchtein, Andrei; Nornberg, Gabrielle; Venzke, Cristiane. Uma hierarquia de testes de convergência de séries baseada no teorema de Kummer. Boletim da Sociedade Paranaense de Matemática, v. 29, p. 83-107, 2011. (link)

BOOK

Maia, Liliane; Nornberg, Gabrielle; Pacella, Filomena. A dynamical system approach for Lane–Emden type problems. Rio de Janeiro, Editora do IMPA, 33º Colóquio Brasileiro de Matemática, 2021. (pdf, classes)

Ph.D. Thesis

Nornberg, G. S.. Methods of the Regularity Theory in the Study of Partial Differential Equations with Natural Growth in the Gradient, 2018 (link)