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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:
58E20 Harmonic maps, etc.
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References:
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