Harmonic Green and Neumann functions for domains bounded by two intersecting circular arcs
Hanxing Lin
Abstract
The parqueting-reflection principle is shown to work for constructing the harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two intersecting circular arcs in C∞ with a particular angle π/n,n∈N∗. With the explicit expressions of the harmonic Green and Neumann functions, we solve the Dirichlet and Neumann boundary problems to the Poisson equation in these domains by applying the Green and Neumann representation formulas.
Topics & Concepts
MathematicsBounded functionHarmonic functionNeumann boundary conditionMathematical analysisNeumann seriesBoundary (topology)Boundary value problemHarmonicHarmonic measureDirichlet distributionPoisson kernelRepresentation (politics)Class (philosophy)Von Neumann architecturePure mathematicsWork (physics)Green SDomain (mathematical analysis)Green's functionDirichlet problemAnalytic and geometric function theoryAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential Equations