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An example of nonhomotopic solutions to the Dirichlet problem for harmonic maps in two dimensions


Authors: Luc Oswald and George Paulik
Journal: Proc. Amer. Math. Soc. 104 (1988), 1267-1270
MSC: Primary 58E20; Secondary 35J25
DOI: https://doi.org/10.1090/S0002-9939-1988-0931745-7
MathSciNet review: 931745
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Abstract: Dirichlet problems of the harmonic map system from the disk into the sphere are presented which have multiple nonhomotopic solutions. In particular, it is shown that for any natural number $ k$ there is a Dirichlet problem which has at least $ k + 1$ nonhomotopic solutions.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0931745-7
Article copyright: © Copyright 1988 American Mathematical Society