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

Morgan Pierre

#### 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