Boundary value problems for Poisson equation on lens and circular triangle domains
Abstract
It is proven that conformal mapping is effective for constructing harmonic Green functions and harmonic Neumann functions in lens domains and circular triangle domains with the specific angle π/n, where n≥2,n∈Z on C. The Dirichlet and Neumann boundary problems of the Poisson equation in these domains are solved by using explicit expressions of the harmonic Green and Neumann functions, and then applying the corresponding representation formulas. Additionally, the explicit expressions of Neumann and Robin functions are modified.
Fields of Study & Subjects
Analytic and geometric function theory
Algebraic and Geometric Analysis
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Complex Variables and Elliptic Equations
- Publisher
- Informa UK Limited
- Pages
- 1–16
- Publication date
- 18 January 2026
- Language
- EN