A computation of Poisson kernels for some standard weighted biharmonic operators in the unit disc

TL;DR

This paper computes explicit Poisson kernels for weighted biharmonic operators in the unit disc, providing new examples and suggesting broader applicability, using computer algebra tools.

Contribution

It introduces explicit formulas for Poisson kernels of weighted biharmonic operators, extending known examples and proposing generalizations.

Findings

Explicit Poisson kernels computed for specific weighted biharmonic operators.

Use of Maxima software facilitated the symbolic computations.

Results suggest potential for broader generalizations of these kernels.

Abstract

We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas for these Poisson kernels to hold true in more generality. Computations have been carried out using the open source computer algebra package Maxima.