Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality−Δmu⩾0inB1(0)−{0}⊂Rn. We give necessary and sufficient conditions on integers n⩾2n⩾2 and m⩾1m⩾1 such that these solutions u   satisfy a pointwise a priori bound as x→0x→0. In this case we show that the optimal bound for u isu(x)=O(Γ(x))asx→0 where Γ   is the fundamental solution of −Δ in RnRn.