Universal inequalities for eigenvalues of a system of elliptic equations of the drifting Laplacian
| Autor: | Rosane Gomes Pereira, Adail de Castro Cavalheiro, Levi Adriano |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Unit sphere
Euclidean space General Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Mathematics::Spectral Theory Type (model theory) Riemannian manifold 01 natural sciences 010101 applied mathematics Combinatorics Domain (ring theory) Projective space Nabla symbol 0101 mathematics Laplace operator Mathematics |
| Zdroj: | Monatshefte für Mathematik. 181:797-820 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-015-0875-8 |
| Popis: | Let \(\Omega \) be a bounded domain in a n-dimensional Euclidean space \(\mathbb {R}^{n}\). We study eigenvalues of an eigenvalue problem of a system of elliptic equations of the drifting Laplacian $$\begin{aligned} \left\{ \begin{array}{ll} \mathbb {L_{\phi }}\mathbf{{u}} + \alpha (\nabla (\mathrm {div}{} \mathbf{{u}}) - \nabla \phi \mathrm {div}{} \mathbf{{u}})= -\bar{\sigma }\mathbf{{u}}, &{} \hbox {in} \,\Omega ; \\ \mathbf{{u}}|_{\,\partial \Omega }=0. \end{array} \right. \end{aligned}$$ Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore, a universal inequality for lower order eigenvalues of the problem is also derived. Finally, we prove an universal inequality type Ashbaugh and Benguria for the drifting Laplacian on Riemannian manifold immersed in an unit sphere or a projective space. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink