Green's functions for certain biharmonic boundary-value problems
Nurbek Kakharman · Complex Variables and Elliptic Equations · 2025
In this paper, 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 a problem where u|∂B=0 and ∂u∂νx−12Δxu=0 on ∂B, which is distinct from classical settings.