Sobolev embeddings on domains involving two types of symmetries
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910835806306304 |
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| author | Cano, Alfredo Flores-Flores, David Hernández-Martínez, Eric |
| author_facet | Cano, Alfredo Flores-Flores, David Hernández-Martínez, Eric |
| contents | 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 $Ω=Ω_1 \times Ω_2$ in $\mathbb{R}^N$ with a cylindrical symmetry, and acting a group $G$ in $Ω_1$, for this situation it is shown that the critical Sobolev exponent increases in the case of embeddings into weighted spaces $L^{q}_{h}(Ω)$. In this paper, we will enunciate several results 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05720 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sobolev embeddings on domains involving two types of symmetries Cano, Alfredo Flores-Flores, David Hernández-Martínez, Eric Analysis of PDEs Classical Analysis and ODEs 46E35, 46B50 G.0.0 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 $Ω=Ω_1 \times Ω_2$ in $\mathbb{R}^N$ with a cylindrical symmetry, and acting a group $G$ in $Ω_1$, for this situation it is shown that the critical Sobolev exponent increases in the case of embeddings into weighted spaces $L^{q}_{h}(Ω)$. In this paper, we will enunciate several results 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. |
| title | Sobolev embeddings on domains involving two types of symmetries |
| topic | Analysis of PDEs Classical Analysis and ODEs 46E35, 46B50 G.0.0 |
| url | https://arxiv.org/abs/2305.05720 |