Abstract.
We prove that for any real number p with \(1< p\leq n-1\), the map \(\frac{x}{|x|} : B^n\to S^{n-1}\) is the unique minimizer of the p-energy functional \(\int_{B^n} |\nabla u|^p dx\) among all maps in \(W^{1,p}(B^n, S^{n-1})\) with boundary value x on \(\partial B^n\).
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Received: 8 November 2000 / Accepted: 4 December 2000 / Published online: 4 May 2001
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HongRID=""ID=""Research of the author was supported by the Australian Research Council, MC. On the minimality of the p-harmonic map \(\frac x{|x|} :B^n\to S^{n-1}\) . Calc Var 13, 459–468 (2001). https://doi.org/10.1007/s005260100082
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DOI: https://doi.org/10.1007/s005260100082