Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets

Gianmichele Di Matteo; Tobias Lamm

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arXiv · 2506.17151

Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets

Gianmichele Di Matteo·Tobias Lamm

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Abstract

Adapting \cite{strz3}, we define generalized $p$-harmonic maps into Riemannian homogeneous targets, a notion of solutions not belonging to the energy space. Restricting our attention to the subcritical range $p$ greater than the domain dimension $n$, we show a uniform $C^{1,\alpha}$-regularity result for a sequence of such maps in the limit $p \searrow n$, assuming a uniform $n$-energy bound on its elements. The method of the proof follows the exact same lines as in \cite{strz3} but we need to check uniformity of estimates not previously considered there.

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Gianmichele Di Matteo, Tobias Lamm. 2025-06-20. Sacks-Uhlenbeck type regularity for subcritical generalized $p$-harmonic maps into Homogeneous targets. https://arxiv.org/abs/2506.17151

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