Advances in Differential Equations

Symmetry breaking for the Dirichlet problem for harmonic maps from the disc into the 2-sphere

Morgan Pierre

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Abstract

We study the relations between symmetry and degree for the Dirichlet problem for harmonic maps from the disc into the $2$-sphere. This allows us to exhibit multiple solutions in many homotopy classes for a wide range of boundary values with symmetries.

Article information

Source
Adv. Differential Equations Volume 10, Number 6 (2005), 675-694.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867839

Mathematical Reviews number (MathSciNet)
MR2133649

Zentralblatt MATH identifier
1101.58014

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Citation

Pierre, Morgan. Symmetry breaking for the Dirichlet problem for harmonic maps from the disc into the 2-sphere. Adv. Differential Equations 10 (2005), no. 6, 675--694. https://projecteuclid.org/euclid.ade/1355867839.


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