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arXiv · 1206.2800

Rotationally symmetric p-harmonic maps from D^2 to S^2

Razvan Gabriel Iagar·Salvador Moll
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Abstract

We consider rotationally symmetric $p$-harmonic maps from the unit disk $D^2\subset\real^2$ to the unit sphere $S^2\subset\real^3$, subject to Dirichlet boundary conditions and with $1<p<\infty$. We show that the associated energy functional admits a unique minimizer which is of class $C^{\infty}$ in the interior and $C^1$ up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler-Lagrange equation and we completely characterize them.

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Razvan Gabriel Iagar, Salvador Moll. 2012-06-13. Rotationally symmetric p-harmonic maps from D^2 to S^2. https://arxiv.org/abs/1206.2800

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