Solving Poisson Equation by Distributional HK-Integral: Prospects and Limitations

Abstract

In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function $\mathcal{D}\left({ℝ}^2\right)$ . Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson’s equation in the upper half space ${ℝ}_{+}^3$ with Dirichlet boundary condition.