Inverse iteration method for higher eigenvalues of the $p$-Laplacian
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911510255632384 |
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| author | Bobkov, Vladimir Galimov, Timur |
| author_facet | Bobkov, Vladimir Galimov, Timur |
| contents | We propose a characterization of a $p$-Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of solutions to consecutive $p$-Poisson equations. The approach relies on the second eigenvalue's minimax properties, but the actual limiting eigenvalue depends on the choice of initial function. The well-posedness and convergence of the iterative scheme are proved. Moreover, we provide the corresponding numerical computations. As auxiliary results, which also have an independent interest, we provide several properties of certain $p$-Poisson problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12836 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse iteration method for higher eigenvalues of the $p$-Laplacian Bobkov, Vladimir Galimov, Timur Analysis of PDEs Numerical Analysis Spectral Theory 35P30, 35J92, 46-08, 47J10, 47J25, 49R05, 65N25 We propose a characterization of a $p$-Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of solutions to consecutive $p$-Poisson equations. The approach relies on the second eigenvalue's minimax properties, but the actual limiting eigenvalue depends on the choice of initial function. The well-posedness and convergence of the iterative scheme are proved. Moreover, we provide the corresponding numerical computations. As auxiliary results, which also have an independent interest, we provide several properties of certain $p$-Poisson problems. |
| title | Inverse iteration method for higher eigenvalues of the $p$-Laplacian |
| topic | Analysis of PDEs Numerical Analysis Spectral Theory 35P30, 35J92, 46-08, 47J10, 47J25, 49R05, 65N25 |
| url | https://arxiv.org/abs/2504.12836 |