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The blow-up of $$p$$-harmonic maps. (English) Zbl 0794.58012
Theorem: Let $$\Omega$$ denote an open bounded set in $$\mathbb{R}^ k$$; if $$u_ n \rightharpoonup u$$ weakly in $$H^{1,p} (\Omega,\mathbb{R}^ k)$$ and $$\lim \partial_ \alpha (| \nabla u_ n|^{p-2} \partial_ \alpha u_ n)=0$$ in the sense of distributions, then $$\partial_ \alpha (|\nabla u|^{p-2} \partial_ \alpha u)=0$$. This has applications in the partial regularity of $$p$$-stationary maps $$\Omega\to S^{k-1}$$.

MSC:
 5.8e+21 Harmonic maps, etc.
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References:
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