@article{Sun_2011, title={Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients}, volume={63}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/2780}, abstractNote={We investigate the Dirichlet weighted eigenvalue problem for a fourth-order elliptic operator with variable coefficients in a bounded domain in $R^n$. We establish a sharp inequality for its eigenvalues. It yields an estimate for the upper bound of the $(k + 1)$-th eigenvalue in terms of the first $k$ eigenvalues. Moreover, we also obtain estimates for some special cases of this problem. In particular, our results generalize the Wang -Xia inequality (J. Funct. Anal. - 2007. - 245) for the clamped plate problem to a fourth-order elliptic operator with variable coefficients.}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Sun, He-Jun}, year={2011}, month={Jul.}, pages={999-1008} }