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- Title
Regularity of Minimizing p-Harmonic Maps Into Spheres and Sharp Kato Inequality.
- Authors
Mazowiecka, Katarzyna; Miśkiewicz, Michał
- Abstract
We study regularity of minimizing |$p$| -harmonic maps |$u \colon B^{3} \to \mathbb{S}^{3}$| for |$p$| in the interval |$[2,3]$|. For a long time, regularity was known only for |$p = 3$| (essentially due to Morrey [ 24 ]) and |$p = 2$| (Schoen–Uhlenbeck [ 29 ]), but recently Gastel [ 7 ] extended the latter result to |$p \in [2,2+\frac{2}{15}]$| using a version of Kato inequality. Here, we establish regularity for a small interval |$p\in [2.961,3]$| by combining Morrey's methods with Hardt and Lin's Extension Theorem [ 11 ]. We also improve on the other result by obtaining regularity for |$p \in [2,p_{0}]$| with |$p_{0} = \frac{3+\sqrt{3}}{2} \approx 2.366$|. In relation to this, we address a question posed by Gastel and prove a sharp Kato inequality for |$p$| -harmonic maps in two-dimensional domains, which is of independent interest.
- Subjects
SPHERES; HARMONIC maps
- Publication
IMRN: International Mathematics Research Notices, 2024, Vol 2024, Issue 5, p3920
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnad139