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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.14620 |
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| _version_ | 1866914707760218112 |
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| author | Mazowiecka, Katarzyna Schikorra, Armin |
| author_facet | Mazowiecka, Katarzyna Schikorra, Armin |
| contents | 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 $π_{n}(\mathbb{S}^\ell)$. 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 to a question raised by Mironescu and Brezis--Mironescu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | s-stability for W^{s,n/s}-harmonic maps in homotopy groups Mazowiecka, Katarzyna Schikorra, Armin Analysis of PDEs Algebraic Topology Functional Analysis 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 $π_{n}(\mathbb{S}^\ell)$. 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 to a question raised by Mironescu and Brezis--Mironescu. |
| title | s-stability for W^{s,n/s}-harmonic maps in homotopy groups |
| topic | Analysis of PDEs Algebraic Topology Functional Analysis |
| url | https://arxiv.org/abs/2308.14620 |