Existence of minimal maps of degree one in $W^{\frac1p,p}(\mathbb S^1,\mathbb S^1)$ for $p \in [p',2]$, where $p' \approx 1.13924$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
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2025
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| _version_ | 1866911087144730624 |
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| author | Kostrzewa, Tomasz Mazowiecka, Katarzyna |
| author_facet | Kostrzewa, Tomasz Mazowiecka, Katarzyna |
| contents | In this note, we show how the results of Mazowiecka--Schikorra, combined with those of Bourgain--Brezis--Mironescu, imply the existence of minimal maps of degree one in $ W^{\frac{1}{p},p}(\mathbb{S}^1,\mathbb{S}^1) $ for $ p \in [p', 2] $, where $ p' \approx 1.13924 $. This provides an affirmative answer in this range to a question posed by Mironescu and Brezis--Mironescu. In order to do so, we complement the results of Mazowiecka--Schikorra by extending them to the case $ n = 1 $ and $ 1 < p < 2 $, which had been excluded there for technical reasons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of minimal maps of degree one in $W^{\frac1p,p}(\mathbb S^1,\mathbb S^1)$ for $p \in [p',2]$, where $p' \approx 1.13924$ Kostrzewa, Tomasz Mazowiecka, Katarzyna Analysis of PDEs In this note, we show how the results of Mazowiecka--Schikorra, combined with those of Bourgain--Brezis--Mironescu, imply the existence of minimal maps of degree one in $ W^{\frac{1}{p},p}(\mathbb{S}^1,\mathbb{S}^1) $ for $ p \in [p', 2] $, where $ p' \approx 1.13924 $. This provides an affirmative answer in this range to a question posed by Mironescu and Brezis--Mironescu. In order to do so, we complement the results of Mazowiecka--Schikorra by extending them to the case $ n = 1 $ and $ 1 < p < 2 $, which had been excluded there for technical reasons. |
| title | Existence of minimal maps of degree one in $W^{\frac1p,p}(\mathbb S^1,\mathbb S^1)$ for $p \in [p',2]$, where $p' \approx 1.13924$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.00529 |