Abstract
We give a sufficient condition on a closed subset Σ⊂Rn for the weighted Poincare inequality (1.5) below to be valid. As an application, we prove that, for any 2≤p<n and any such closed subset Σ⊂Rn, if u∈C1(Ω ∖ Σ, N) ∩ W1,p (Ω, N) is a stationary p-harmonic map such that ∫Ω|Du|p(x) dx is sufficiently small, then u∈C1(Ω, N). This extends previously known removal singularity theorems for p-harmonic maps.
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