As a third-year mathematics student at SDU University, my research centers on explicit Green’s functions for polyharmonic boundary value problems, supervised by Dr. Nurbek Kakharman. My recent derivation of Green’s functions for the Navier problem in the biharmonic equation required mastering advanced functional analysis and PDE theory, while innovating techniques for non-local boundary conditions-an achievement rare for undergraduates.

The Hong Kong Laureate Forum is a pivotal opportunity to engage with pioneers in PDEs and functional analysis. I am eager to discuss my work on Green’s functions, which bridges abstract theory and applied problems (e.g., elasticity models), and to learn from laureates tackling modern challenges in elliptic PDEs.

Beyond research, I lead study groups to share Green’s function applications, fostering collaborative learning. This forum would accelerate my growth as a future PhD candidate in PDEs, providing exposure to cutting-edge methods and global perspectives. I am confident my unique blend of theoretical rigor and applied intuition will contribute meaningfully to discussions while shaping my trajectory toward advancing PDE solutions.

SDU University

In my work, we present an explicit form of Green's functions for two biharmonic boundary value problems in the multidimensional ball. Specifically, we obtain exact representations of Green's functions for a non-standard Robin-type problem, where the boundary conditions depend on the dimension $n,$ and the Navier problem, in which both the function and its Laplacian vanish on the boundary.

For the Navier case, our results improve upon the recent work of V.V. Karachik [Comp. Var. Eell. Eq. (2021), 654–668], where the Green's function for the Navier problem is represented using an integral expression.