Vectorial Kato inequality for $p$-harmonic maps with optimal constant
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915184938844160 |
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| author | Gastel, Andreas Mazowiecka, Katarzyna Miśkiewicz, Michał |
| author_facet | Gastel, Andreas Mazowiecka, Katarzyna Miśkiewicz, Michał |
| contents | We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how this inequality can be used in the study of regularity of $p$-harmonic maps. Furthermore, in the case of $p$-harmonic maps from $B^3$ to $\mathbb{S}^3$, we enhance the known range of $p$ values for which regularity is achieved. Specifically, we establish that for $p \in [2, 2.642]$, minimizing $p$-harmonic maps must be regular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_05038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vectorial Kato inequality for $p$-harmonic maps with optimal constant Gastel, Andreas Mazowiecka, Katarzyna Miśkiewicz, Michał Analysis of PDEs Differential Geometry 58E20, 35B65, 35J60 We derive the sharp vectorial Kato inequality for $p$-harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$-harmonic functions by Chang, Chen, and Wei. As an application we demonstrate how this inequality can be used in the study of regularity of $p$-harmonic maps. Furthermore, in the case of $p$-harmonic maps from $B^3$ to $\mathbb{S}^3$, we enhance the known range of $p$ values for which regularity is achieved. Specifically, we establish that for $p \in [2, 2.642]$, minimizing $p$-harmonic maps must be regular. |
| title | Vectorial Kato inequality for $p$-harmonic maps with optimal constant |
| topic | Analysis of PDEs Differential Geometry 58E20, 35B65, 35J60 |
| url | https://arxiv.org/abs/2503.05038 |