Singular extension of critical Sobolev mappings under an exponential weak-type estimate
| Autor: | Bulanyi, Bohdan, Van Schaftingen, Jean |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | J. Funct. Anal. 288 (2025), n{\deg}1, 110681 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jfa.2024.110681 |
| Popis: | 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. Comment: 21 pages, minor corrections |
| Databáze: | arXiv |
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