Isolated singularities of polyharmonic inequalities

We study nonnegative classical solutions u of the polyharmonic inequality − mu 0 inB1(0) − {0} ⊂ Rn. We give necessary and sufficient conditions on integers n 2 and m 1 such that these solutions u satisfy a pointwise a priori bound as x→0. In this case we show that the optimal bound for u is u(x) = O Γ (x) as x→0 where Γ is the fundamental solution of − in Rn. © 2011 Elsevier Inc. All rights reserved