For and , we prove that a map from an open domain into the unit -sphere, which solves a generalized version of the harmonic map equation, is smooth, provided that and are both sufficiently small. This extends a result of Almeida . The proof is based on an inverse Holder inequality technique.
Submitted December 13, 2002. Published January 2, 2003.
Math Subject Classifications: 58E20.
Key Words: Generalized harmonic maps, regularity.
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|Roger Moser |
MPI for Mathematics in the Sciences
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