Singular extension of critical Sobolev mappings under an exponential weak-type estimate
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929599334580224 |
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| author | Bulanyi, Bohdan Van Schaftingen, Jean |
| author_facet | Bulanyi, Bohdan Van Schaftingen, Jean |
| contents | Given $m \in \mathbb{N} \setminus \{0\}$ and a compact Riemannian manifold $\mathcal{N}$, we construct for every map $u$ in the critical Sobolev space $W^{m/(m + 1), m + 1} (\mathbb{S}^m, \mathcal{N})$, a map $U : \mathbb{B}^{m + 1} \to \mathcal{N}$ whose trace is $u$ and which satisfies an exponential weak-type Sobolev estimate. The result and its proof carry on to the extension to a half-space of maps on its boundary hyperplane and to the extension to the hyperbolic space of maps on its boundary sphere at infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12874 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Singular extension of critical Sobolev mappings under an exponential weak-type estimate Bulanyi, Bohdan Van Schaftingen, Jean Analysis of PDEs Classical Analysis and ODEs Functional Analysis 58D15 (Primary), 46E35 (Secondary) Given $m \in \mathbb{N} \setminus \{0\}$ and a compact Riemannian manifold $\mathcal{N}$, we construct for every map $u$ in the critical Sobolev space $W^{m/(m + 1), m + 1} (\mathbb{S}^m, \mathcal{N})$, a map $U : \mathbb{B}^{m + 1} \to \mathcal{N}$ whose trace is $u$ and which satisfies an exponential weak-type Sobolev estimate. The result and its proof carry on to the extension to a half-space of maps on its boundary hyperplane and to the extension to the hyperbolic space of maps on its boundary sphere at infinity. |
| title | Singular extension of critical Sobolev mappings under an exponential weak-type estimate |
| topic | Analysis of PDEs Classical Analysis and ODEs Functional Analysis 58D15 (Primary), 46E35 (Secondary) |
| url | https://arxiv.org/abs/2309.12874 |