We study s -dependence for minimizing W^{s,n/s} -harmonic maps u\colon \mathbb{S}^{n} \to \mathbb{S}^{\ell} in homotopy classes. Sacks–Uhlenbeck theory shows that, for each s , minimizers exist in a generating subset of \pi_{n}(\mathbb{S}^{\ell}) . We show that this generating subset can be chosen locally constant in s . We also show that as s varies, the minimal W^{s,n/s} -energy in each homotopy class changes continuously. In particular, we provide progress on a question raised by Mironescu [in: Perspectives in nonlinear partial differential equations (2007), 413–436] and Brezis–Mironescu [Sobolev maps to the circle (2021)].

Katarzyna Mazowiecka

Armin Schikorra

Annales de l Institut Henri Poincaré C Analyse Non Linéaire

The Nonlinear Analysis section of the Annales de l'Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.

The Annales de l'Institut Henri Poincaré (C) Analyse Non Lineaire is an international journal established in 1983, focusing on the field of nonlinear analysis. It publishes original and high-quality research articles that cover all domains related to nonlinear analysis, particularly applicable to partial differential equations, mechanics, physics, and economics, while also addressing numerical aspects.

《Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire》是一本国际期刊，成立于1983年，专注于非线性分析领域，发表原创且高质量的研究文章。期刊涵盖与非线性分析相关的所有领域，特别是偏微分方程、力学、物理学和经济学等应用，同时也关注数值分析的相关内容。

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$s$-stability for $W^{s,n/s}$-harmonic maps in homotopy groups

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MATHEMATICS, APPLIED	1