PreprintCC BY 4.0arXiv
Regularity of minimizing p-harmonic maps from B3 to 𝕊3
Abstract
We prove that every minimizing p-harmonic map from B3 into 𝕊3 is locally C1,α for some α∈(0,1), for every p>p0, where p0=(7−√(17))/2≈ 1.44. This closes the gap between the previously established regularity ranges [2,2.642]∪[2.961,3] and, in particular, yields full interior regularity for all p≥2. The result also extends regularity to the subquadratic range p0<p<2.
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BibTeX
@misc{mazowiecka2026regularity,
title = {{Regularity of minimizing $p$-harmonic maps from $B^3$ to $\mathbbS^3$}},
author = {Katarzyna Mazowiecka and Michał Miśkiewicz and Patryk Tokarczuk},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27516},
eprint = {2609.27516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27516},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Regularity of minimizing p-harmonic maps from B^3 to 𝕊^3
AU - Katarzyna Mazowiecka
AU - Michał Miśkiewicz
AU - Patryk Tokarczuk
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27516
UR - https://arxiv.org/abs/2609.27516
AB - We prove that every minimizing p-harmonic map from B^3 into 𝕊^3 is locally C^1,α for some α∈(0,1), for every p>p_0, where p_0=(7−√(17))/2≈ 1.44. This closes the gap between the previously established regularity ranges [2,2.642]∪[2.961,3] and, in particular, yields full interior regularity for all p≥2. The result also extends regularity to the subquadratic range p_0<p<2.
ER -