Abstract
We study nonnegative classical solutions u of the polyharmonic inequality − Δ m u ⩾ 0 in B 1 ( 0 ) − { 0 } ⊂ R n . 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 −Δ in R n .
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