Characterizing Sobolev Homeomorphic Extensions via Internal Distances
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908286057447424 |
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| author | Koski, Aleksis Onninen, Jani Xu, Haiqing |
| author_facet | Koski, Aleksis Onninen, Jani Xu, Haiqing |
| contents | We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasiconvex target domains $\mathbb Y$, any homeomorphism $φ\colon \partial \mathbb{D} \to \partial \mathbb Y$ that admits a continuous $W^{1,p}$-extension to the unit disk $\mathbb{D}$ also admits a $W^{1,p}$-homeomorphic extension. These Sobolev variants of the classical Jordan-Schönflies theorem are essential for ensuring the well-posedness of variational problems arising in Nonlinear Elasticity and Geometric Function Theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizing Sobolev Homeomorphic Extensions via Internal Distances Koski, Aleksis Onninen, Jani Xu, Haiqing Complex Variables 46E35, 42B25, 58E20 We give a full characterization of embeddings of the unit circle that admit a Sobolev homeomorphic extension to the unit disk. As a direct corollary, we establish that for quasiconvex target domains $\mathbb Y$, any homeomorphism $φ\colon \partial \mathbb{D} \to \partial \mathbb Y$ that admits a continuous $W^{1,p}$-extension to the unit disk $\mathbb{D}$ also admits a $W^{1,p}$-homeomorphic extension. These Sobolev variants of the classical Jordan-Schönflies theorem are essential for ensuring the well-posedness of variational problems arising in Nonlinear Elasticity and Geometric Function Theory. |
| title | Characterizing Sobolev Homeomorphic Extensions via Internal Distances |
| topic | Complex Variables 46E35, 42B25, 58E20 |
| url | https://arxiv.org/abs/2503.21132 |