Solution operator of inhomogenuous Dirichlet problem in the unit ball

TL;DR

This paper estimates the norms of an integral operator associated with the Green function for the Poisson equation in the unit ball, providing insights into the behavior of solutions with zero boundary conditions.

Contribution

It introduces new norm estimates for the Green function integral operator in the context of the inhomogeneous Dirichlet problem in the unit ball.

Findings

Derived explicit bounds for the integral operator norms

Enhanced understanding of solution regularity for the Poisson equation

Potential applications to boundary value problem analysis

Abstract

In this paper we estimate norms of integral operator induced with Green function related to the Poisson equation in the unit ball with vanishing boundary data.