In this paper we investigate estimates about the Laplace operator of harmonic maps, focusing outside the singularities through spherical coordinates. These estimates can be used in the general Ericksen--Leslie system to obtain higher-order estimates. We consider the problem subject to the $\mathbb{T}^2$ and $\mathbb{T}^3$ boundary conditions.
Global Well-posedness and Long-time Behavior of the General Ericksen--Leslie System in 2D under a Magnetic Field
Integrable Systems and Harmonic Maps into Lie Groups
Partial regularity for harmonic maps, and related problems
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