Decoupling for finite type phases in higher dimensions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866918224766959616 |
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| author | Gao, Chuanwei Li, Zhuoran Zhao, Tengfei Zheng, Jiqiang |
| author_facet | Gao, Chuanwei Li, Zhuoran Zhao, Tengfei Zheng, Jiqiang |
| contents | In this paper, we establish an $\ell^2$ decoupling inequality for the hypersurface \[\Big\{(ξ_1,...,ξ_{n-1},ξ_1^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\}\]associated with the decomposition adapted to hypersufaces of finite type, where $n\geq 2$ and $m\geq 4$ is an even number. The key ingredients of the proof include an $\ell^2$ decoupling inequality for the hypersurfaces
\[\Big\{(ξ_1,...,ξ_{n-1},ϕ_1(ξ_1)+...+ϕ_s(ξ_s)+ξ_{s+1}^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\},\] $0 \leq s \leq n-1$, with $ϕ_1,...,ϕ_s$ being $m$-nondegenerate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2202_11326 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Decoupling for finite type phases in higher dimensions Gao, Chuanwei Li, Zhuoran Zhao, Tengfei Zheng, Jiqiang Analysis of PDEs In this paper, we establish an $\ell^2$ decoupling inequality for the hypersurface \[\Big\{(ξ_1,...,ξ_{n-1},ξ_1^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\}\]associated with the decomposition adapted to hypersufaces of finite type, where $n\geq 2$ and $m\geq 4$ is an even number. The key ingredients of the proof include an $\ell^2$ decoupling inequality for the hypersurfaces \[\Big\{(ξ_1,...,ξ_{n-1},ϕ_1(ξ_1)+...+ϕ_s(ξ_s)+ξ_{s+1}^m+...+ξ_{n-1}^m): (ξ_1,...,ξ_{n-1}) \in [0,1]^{n-1}\Big\},\] $0 \leq s \leq n-1$, with $ϕ_1,...,ϕ_s$ being $m$-nondegenerate. |
| title | Decoupling for finite type phases in higher dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2202.11326 |