The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866909077464940544 |
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| author | Bozorgnia, Farid Bungert, Leon Tenbrinck, Daniel |
| author_facet | Bozorgnia, Farid Bungert, Leon Tenbrinck, Daniel |
| contents | In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. Subsequently, we present consistent monotone schemes to approximate infinity ground states and higher eigenfunctions on grids. We prove that our method converges (up to a subsequence) to a viscosity solution of the eigenvalue problem, and perform numerical experiments which investigate theoretical conjectures and compute eigenfunctions on a variety of different domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08127 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme Bozorgnia, Farid Bungert, Leon Tenbrinck, Daniel Numerical Analysis Analysis of PDEs Spectral Theory 35D40, 35P30, 65N06, 65N12, 65N25 In this work, we present an alternative formulation of the higher eigenvalue problem associated to the infinity Laplacian, which opens the door for numerical approximation of eigenfunctions. A rigorous analysis is performed to show the equivalence of the new formulation to the traditional one. Subsequently, we present consistent monotone schemes to approximate infinity ground states and higher eigenfunctions on grids. We prove that our method converges (up to a subsequence) to a viscosity solution of the eigenvalue problem, and perform numerical experiments which investigate theoretical conjectures and compute eigenfunctions on a variety of different domains. |
| title | The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme |
| topic | Numerical Analysis Analysis of PDEs Spectral Theory 35D40, 35P30, 65N06, 65N12, 65N25 |
| url | https://arxiv.org/abs/2004.08127 |