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1988•Proceedings of the American Mathematical SocietyOpen access

An Example of Nonhomotopic Solutions to the Dirichlet Problem for Harmonic Maps in Two Dimensions

Luc Oswald, George Paulik

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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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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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Available 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.

Key concepts: Dirichlet problem, Dirichlet distribution, Dirichlet's energy, Mathematics, Harmonic, Dirichlet's principle, Harmonic map, Dirichlet eigenvalue

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