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A weighted Poincaré inequality and removable singularities for harmonic maps

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Abstract.

We give a sufficient condition on a closed subset Σ⊂R n for the weighted Poincaré inequality (1.5) below to be valid. As an application, we prove that, for any 2≤p<n and any such closed subset Σ⊂R n, if u∈C 1(Ω ∖ Σ, N) ∩ W 1,p (Ω, N) is a stationary p-harmonic map such that ∫Ω|Du|p(x) dx is sufficiently small, then u∈C 1(Ω, N). This extends previously known removal singularity theorems for p-harmonic maps.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington KY, 40506, USA

    Changyou Wang

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  1. Changyou Wang
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Correspondence to Changyou Wang.

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Mathematics Subject Classification (2000): 58E20, 58J05, 35J60

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Wang, C. A weighted Poincaré inequality and removable singularities for harmonic maps. manuscripta math. 112, 259–270 (2003). https://doi.org/10.1007/s00229-003-0403-3

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  • DOI: https://doi.org/10.1007/s00229-003-0403-3

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