Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n
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2016-03-08
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Universidade Federal de Goiás
Resumo
In this work, we study eigenvalues of poly-drifting laplacian on compact
Riemannian manifolds with boundary (possibly empty). Here, we bring a
universal inequality for the eigenvalues of the poly-drifting operator on compact
domains in an Euclidean spaceRn. Besides,weintroduce universal inequalities for
eigenvalues of poly-drifting operator on compact domains in a unit n-sphere Sn.
We give an universal inequality for lower order eigenvalues of the poly-drifting
operator inRn and Sn. Moreover, 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. Let
be a bounded domain in a n-dimensional
Euclidean space Rn. We study eigenvalues of an eigenvalue problem of a system
of elliptic equations of the drifting laplacian
8>><>>:
L u+ (r(divu)r divu) = ¯ u; in
;
uj@
= 0
Estimates for eigenvalues of the above eigenvalue problem are obtained. Furthermore,
a universal inequality for lower order eigenvalues of the problem is also
derived.
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Citação
PEREIRA, R. G. Desigualdades universais para autovalores do polidrifting laplaciano em dominios compactos do R^n e S^n. 2016. 116 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.