A Dirichlet type problem for complex polyharmonic functions

TL;DR

This paper extends holomorphically polyharmonic functions from a real ball to a union of rotated balls in the complex plane and solves a Dirichlet problem with boundary conditions on rotated spheres.

Contribution

It introduces a method to extend polyharmonic functions holomorphically and solves a Dirichlet problem on complex unions of rotated spheres, advancing boundary value problem theory.

Findings

Holomorphic extension of polyharmonic functions achieved

Solution to Dirichlet problem on union of rotated spheres

New techniques for boundary value problems in complex analysis

Abstract

We extend holomorphically polyharmonic functions on a real ball to a complex set being the union of rotated balls. We solve a Dirichlet type problem for complex polyharmonic functions with the boundary condition given on the union of rotated spheres.