Estimates for the first eigenvalue of the one-dimensional $p$-Laplacian
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911230342463488 |
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| author | Kajikiya, Ryuji Takeuchi, Shingo |
| author_facet | Kajikiya, Ryuji Takeuchi, Shingo |
| contents | In the present paper, we study the first eigenvalue $λ(p)$ of the one-dimensional $p$-Laplacian in the interval $(-1,1)$. We give an upper and lower estimate of $λ(p)$ and study its asymptotic behavior as $p \to 1+0$ or $p \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates for the first eigenvalue of the one-dimensional $p$-Laplacian Kajikiya, Ryuji Takeuchi, Shingo Analysis of PDEs Classical Analysis and ODEs 34B09, 34L30, 26D05, 33B10 In the present paper, we study the first eigenvalue $λ(p)$ of the one-dimensional $p$-Laplacian in the interval $(-1,1)$. We give an upper and lower estimate of $λ(p)$ and study its asymptotic behavior as $p \to 1+0$ or $p \to \infty$. |
| title | Estimates for the first eigenvalue of the one-dimensional $p$-Laplacian |
| topic | Analysis of PDEs Classical Analysis and ODEs 34B09, 34L30, 26D05, 33B10 |
| url | https://arxiv.org/abs/2412.04740 |