Genival Francisco Fernandes
da Silva Jr.
Assistant Professor of Mathematics
Texas A&M University - San Antonio
Department of Mathematics
Classroom Hall, Room 314 U
Email: gdasilva@tamusa.edu
I completed my PhD in Mathematics at Washington University in St. Louis under direction of
Prof. Matt Kerr, after that I was a postdoc at Imperial College London under supervision of Prof.
Tom Coates and Prof.
Alessio Corti.
Research Interests
Analysis of PDE
My research interests lie in nonlinear elliptic partial differential equations and elliptic systems, with a particular focus on the existence and regularity of solutions, approached through both variational and non-variational methods.
Below is a list of research subtopics I frequently consider:
- Degenerate elliptic equations (e.g., those involving the p-Laplacian)
- Semilinear elliptic equations
- Shape optimization problems
- Variational approaches to elliptic problems
- Regularity theory for (possibly degenerate) elliptic equations
I maintain a list of open question that come up during my research here: Open problems in Elliptic PDEs.
Research Papers
- A nonlinear problem related to optimal insulation.
Under peer review - 2025
- A New proof of the p'-conjecture in the plane via a priori estimates.
Under peer review - 2025
- Quasilinear Hardy-Hénon equation with power source.
Under peer review - 2025
- An inhomogeneous p-laplacian equation with a Hardy potential.
Under peer review - 2024
- Radially symmetric solutions to a Lane-Emden type system.
Under peer review 2024
- An elliptic equation with power nonlinearity and degenerate coercivity.
Journal of Elliptic and Parabolic Equations, 2025, DOI: 10.1007/s41808-025-00341-8
- On an elliptic system with singular nonlinearity.
European Journal of Mathematics, 2025, DOI: 10.1007/s40879-025-00840-x
- Quasilinear elliptic equations with superlinear convection.
Journal of Mathematical Analysis and Applications, 2025, DOI: 10.1016/j.jmaa.2025.130005
- Continuous weak solutions to the Ideal Hall equation
Preprint - 2023
- The Complexity of Higher Chow Groups
Canadian Math. Bull. , 2023, DOI: 10.4153/S0008439522000509
with James Lewis
- The Chow motive of a Fano variety of k-planes
Communications in Algebra , 2023, DOI: 10.1080/00927872.2023.2252078
with James Lewis
- Known cases of the Hodge conjecture (expository)
arXiv
- On the topology of Fano smoothings
Interactions with Lattice Polytopes, Springer, 2022, DOI: 978-3-030-98327-7
with Tom Coates and Alessio Corti
- On the monodromy of elliptic surfaces
Israel Journal of Mathematics, 2022, DOI: s11856-022-2458-4
- Notes on the Hodge Conjecture for Fermat Varieties
Experimental Results , Volume 2 , 2021 , e22, DOI: 10.1017/exp.2021.14
- On the arithmetic of Landau-Ginzburg model of a certain class of threefolds
Communications in Number Theory and Physics 13, No. 1, 2019, DOI: 10.4310/cntp.2019.v13.n1.a5
- Arithmetic of degenerating principal variations of Hodge structure: examples arising from mirror symmetry and middle convolution,
Canadian Journal of Mathematics 68, 2014, DOI: 10.4153/CJM-2015-020-4
with Matt Kerr and Greg Pearstein
Books
Teaching
- Differential Equations
- Spring 2023
Expository