About Bounds for Eigenvalues of the Laplacian with Density
Let denote a compact, connected Riemannian manifold of dimension ∈ ℕ. We assume that has a smooth and connected boundary. Denote by and d, respectively, the Riemannian metric on and the associated volume element. Let Δ be the Laplace operator on equipped with the weighted volume form d:= e⁻ʰd....
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210758 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | About Bounds for Eigenvalues of the Laplacian with Density. Aïssatou Mossèle Ndiaye. SIGMA 16 (2020), 090, 8 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862748892246835200 |
|---|---|
| author | Ndiaye, Aïssatou Mossèle |
| author_facet | Ndiaye, Aïssatou Mossèle |
| citation_txt | About Bounds for Eigenvalues of the Laplacian with Density. Aïssatou Mossèle Ndiaye. SIGMA 16 (2020), 090, 8 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let denote a compact, connected Riemannian manifold of dimension ∈ ℕ. We assume that has a smooth and connected boundary. Denote by and d, respectively, the Riemannian metric on and the associated volume element. Let Δ be the Laplace operator on equipped with the weighted volume form d:= e⁻ʰd. We are interested in the operator Lₕ⋅ :=e⁻ʰ⁽ᵅ⁻¹⁾(Δ⋅+α(∇h, ∇⋅)), where α > 1 and ∈ ²() are given. The main result in this paper states the existence of upper bounds for the eigenvalues of the weighted Laplacian Lₕ with the Neumann boundary condition if the boundary is non-empty.
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| first_indexed | 2026-04-17T19:56:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210758 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T19:56:16Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ndiaye, Aïssatou Mossèle 2025-12-17T14:27:27Z 2020 About Bounds for Eigenvalues of the Laplacian with Density. Aïssatou Mossèle Ndiaye. SIGMA 16 (2020), 090, 8 pages 1815-0659 2020 Mathematics Subject Classification: 35P15; 58J50 arXiv:2002.03698 https://nasplib.isofts.kiev.ua/handle/123456789/210758 https://doi.org/10.3842/SIGMA.2020.090 Let denote a compact, connected Riemannian manifold of dimension ∈ ℕ. We assume that has a smooth and connected boundary. Denote by and d, respectively, the Riemannian metric on and the associated volume element. Let Δ be the Laplace operator on equipped with the weighted volume form d:= e⁻ʰd. We are interested in the operator Lₕ⋅ :=e⁻ʰ⁽ᵅ⁻¹⁾(Δ⋅+α(∇h, ∇⋅)), where α > 1 and ∈ ²() are given. The main result in this paper states the existence of upper bounds for the eigenvalues of the weighted Laplacian Lₕ with the Neumann boundary condition if the boundary is non-empty. This paper is part of the author's Ph.D. Thesis under the direction of Professor Bruno Colbois (Neuchâtel University). The author wishes to express her thanks to her supervisor for suggesting the problem. She is also grateful to the anonymous referee whose suggestions and remarks greatly improved this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications About Bounds for Eigenvalues of the Laplacian with Density Article published earlier |
| spellingShingle | About Bounds for Eigenvalues of the Laplacian with Density Ndiaye, Aïssatou Mossèle |
| title | About Bounds for Eigenvalues of the Laplacian with Density |
| title_full | About Bounds for Eigenvalues of the Laplacian with Density |
| title_fullStr | About Bounds for Eigenvalues of the Laplacian with Density |
| title_full_unstemmed | About Bounds for Eigenvalues of the Laplacian with Density |
| title_short | About Bounds for Eigenvalues of the Laplacian with Density |
| title_sort | about bounds for eigenvalues of the laplacian with density |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210758 |
| work_keys_str_mv | AT ndiayeaissatoumossele aboutboundsforeigenvaluesofthelaplacianwithdensity |