Geodesic
Inequalities for Lower-Order Eigenvalues of a Fourth-Order Elliptic Operator
Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 286-294

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In this paper, we investigate the Dirichlet weighted eigenvalues problem of a fourth-order elliptic operator with variable coefficients on a bounded domain with smooth boundary in $\mathbb{R}^n$. We establish some inequalities for lower-order eigenvalues of this problem. In particular, our results contain an inequality for eigenvalues of the biharmonic operator derived by Cheng, Huang, and Wei.
Keywords: eigenvalue, elliptic operator, biharmonic operator, Laplace operator. 
@article{MZM_2013_93_2_a12,
     author = {He-Jun Sun},
     title = {Inequalities for {Lower-Order} {Eigenvalues} of a {Fourth-Order} {Elliptic} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {286--294},
     publisher = {mathdoc},
     volume = {93},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a12/}
}
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He-Jun Sun. Inequalities for Lower-Order Eigenvalues of a Fourth-Order Elliptic Operator. Matematičeskie zametki, Tome 93 (2013) no. 2, pp. 286-294. http://geodesic.mathdoc.fr/item/MZM_2013_93_2_a12/