Abstract:We show that $id:\mathbb{S}^1 \to \mathbb{S}^1$ is \emph{not} a minimizing $W^{s,\frac{1}{s}}$-harmonic map for $s \in (0,\frac{1}{8}$). On the other hand, for $s \in (\frac{1}{3},1)$ it is a local minimizing map, and for $s\in [\frac{1}{2}-\varepsilon,\frac{1}{2}+\varepsilon]$ it is a global minimizer. The usual extension or Fourier techniques being unavailable, our argument relies instead of stability analysis in $s$.
From: Armin Schikorra [view email]
[v1]
Sun, 14 Jun 2026 07:21:05 UTC (45 KB)
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