Removable singularity of the polyharmonic equation

Let x₀∈Ω⊂Rⁿ, n≥2, be a domain and let m≥2. We will prove that a solution u of the polyharmonic equation Δ^mu=0 in Ω?{x₀} has a removable singularity at x₀ if and only if as |x−x₀|→0 for n≥3 and as |x−x₀|→0 for n=2. For m≥2 we will also prove that u has a removable singularity at x₀ if |u(x)|=o(|x−x₀|^2m−n) as |x−x₀|→0 for n≥3 and |u(x)|=o(|x−x₀|^2m−2log(|x−x₀|⁻¹)) as |x−x₀|→0 for n=2.