Solving Poisson's equation for the standard weighted Laplacian in the unit disc

2013/06/10 by Behm Gustav, Behm, Gustav
Computer Science · Mathematics · #35J08 (Secondary) #35J25 (Primary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1306.2199

openalex publication_date 2013/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We will find Green's function for the standard weighted Laplacian and use the corresponding Green's potential to solve Poisson's equation in the unit disc with zero boundary values, in the sense of radial L¹-means, for complex Borel measures μ satisfying the condition ∫_\mathbbD (1-|w|²)^α+1 d|μ|(w) < ∞ for α>-1.

Related

• Something about Poisson and Dirichlet
• Cauchy transform and Poisson's equation
• Green function for the Poisson equation in a general case of astrophysical interest
• Generalized Poisson kernel and solution of the Dirichlet problem for the radial Schrödinger equation
• On the Green function and Poisson integrals of the Dunkl Laplacian