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Regularity of p-harmonic maps from the p-dimensional ball into a sphere

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Abstract

We prove that, forp≥2, all weaklyp-harmonic mapsu=(u 1,...,u n ) from thep-dimensional ball into a sphere, i.e. weak solutions of classW 1,p of the constrained eliptic system

$$\begin{gathered} - div(|\nabla u|^{p - 2} \nabla u_i ) = u_i |\nabla u|^p \hfill \\ \sum {(u_i )} ^2 = 1, \hfill \\ \end{gathered} $$

are Hölder continuous. This result is an analogue of an earlier theorem of F. Hélein for the casep=2.

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Authors and Affiliations

  1. Instytut Matematyki, Universytet Warszawski, ul. Banacha 2, 02-097, Warszawa, Poland

    Pawel Strzelecki

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  1. Pawel Strzelecki
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This work is partially supported by KBN grant no. 2 1057 91 01

This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990.

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Strzelecki, P. Regularity of p-harmonic maps from the p-dimensional ball into a sphere. Manuscripta Math 82, 407–415 (1994). https://doi.org/10.1007/BF02567710

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  • DOI: https://doi.org/10.1007/BF02567710

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