Sobolev embeddings on domains involving two types of symmetries
| Autor: | Cano, Alfredo, Flores-Flores, David, Hernández-Martínez, Eric |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | It is well known that Sobolev embeddings can be improved in the presence of symmetries. In this article, we considere the situation in which given a domain $\Omega=\Omega_1 \times \Omega_2$ in $\mathbb{R}^N$ with a cylindrical symmetry, and acting a group $G$ in $\Omega_1$, for this situation it is shown that the critical Sobolev exponent increases in the case of embeddings into weighted spaces $L^{q}_{h}(\Omega)$. In this paper, we will enunciate several results based from theorems by Wang, helping us with results by Hebey-Vaugon related to compact embeddings of a Sobolev space with radially symmetric functions into some weighted space $L^{q}$, with $q$ higher than the usual critical exponent. Comment: 17 pages |
| Databáze: | arXiv |
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