Desigualdades universais para autovalores do operador poli-harmônico
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Data
2012-03-09
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Universidade Federal de Goiás
Resumo
In this work, we study eigenvalues of polyharmonic operators on compact Riemannian manifolds with boundary (possibly empty). Here, we bring in a universal inequality for the eigenvalues of the polyharmonic operator on compact
domains in an Euclidean space Rn. This inequality controls the kth eigenvalue by the lower eigenvalues, independently of the particular geometry of the domain. Besides, a inequality we present covers the important Yang inequality on eigenvalues of the Dirichlet Laplacian. Finally, we introduce universal inequalities for eigenvalues of polyharmonic operator on compact domains in a unit n-sphere Sn. NOTE: Programs do not copy or copy errors with certain symbols, formulas, formatting, etc ..., n of Rn and Sn are overwritten. View all content by clicking pdf - dissertation at the bottom of the screen.
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Citação
PEREIRA, Rosane Gomes. Universal bounds for eigenvalues of the polyharmonic
operator. 2012. 77 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2012.