Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913466983383040 |
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| author | Huang, Xia Li, Yuan Zhou, Xianmei |
| author_facet | Huang, Xia Li, Yuan Zhou, Xianmei |
| contents | In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane-Emden equation
\begin{equation*}
Δ^{2} u=u^{p}
\quad
\quad \text{in} \ \mathbb{R}^{N}\setminus Z,
\end{equation*}
where $N\geq5$, $1<p\leq\frac{N+4}{N-4}$, and the singular set $Z$ represents a closed and proper subset of $ \left\lbrace x_{1}=0\right\rbrace $. The symmetry and monotonicity properties of the singular solutions will be given by taking advantage of the moving plane method and the approach of moving spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06692 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set Huang, Xia Li, Yuan Zhou, Xianmei Analysis of PDEs In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane-Emden equation \begin{equation*} Δ^{2} u=u^{p} \quad \quad \text{in} \ \mathbb{R}^{N}\setminus Z, \end{equation*} where $N\geq5$, $1<p\leq\frac{N+4}{N-4}$, and the singular set $Z$ represents a closed and proper subset of $ \left\lbrace x_{1}=0\right\rbrace $. The symmetry and monotonicity properties of the singular solutions will be given by taking advantage of the moving plane method and the approach of moving spheres. |
| title | Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.06692 |