Estimates of eigenvalues of elliptical differential problems in divergence form
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917316167467008 |
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| author | FIlho, Marcio C. Araújo Miranda, Juliana F. R. Silva, Cristiano S. |
| author_facet | FIlho, Marcio C. Araújo Miranda, Juliana F. R. Silva, Cristiano S. |
| contents | In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lamé and the Laplacian operator. Furthermore, we also give universal estimates of eigenvalues for a class of fourth-order elliptic differential problems in divergence form, which encloses the well-known bi-Laplacian operator. In both cases, as applications, we obtain the gap between consecutive eigenvalues as well as an upper bound for each eigenvalue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_05245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Estimates of eigenvalues of elliptical differential problems in divergence form FIlho, Marcio C. Araújo Miranda, Juliana F. R. Silva, Cristiano S. Differential Geometry Spectral Theory Primary 47A75, Secondary 47F05, 35P15, 53C24, 53C25 In this paper, we compute universal estimates of eigenvalues for a class of coupled systems of elliptic differential equations in divergence form on a bounded domain in Euclidean space, which includes the well-known Lamé and the Laplacian operator. Furthermore, we also give universal estimates of eigenvalues for a class of fourth-order elliptic differential problems in divergence form, which encloses the well-known bi-Laplacian operator. In both cases, as applications, we obtain the gap between consecutive eigenvalues as well as an upper bound for each eigenvalue. |
| title | Estimates of eigenvalues of elliptical differential problems in divergence form |
| topic | Differential Geometry Spectral Theory Primary 47A75, Secondary 47F05, 35P15, 53C24, 53C25 |
| url | https://arxiv.org/abs/2603.05245 |