Existence of Solutions to Poisson's Equation
Mary Hanley · Canadian Mathematical Bulletin · 2008
Abstract Let Ω be a domain in ℝn(n≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasureμon ℝn, there is a functionuwith specified boundary conditions that satisfies the Poisson equation Δu=μon Δ in the sense of distributions.