Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients
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...
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| Date: | 2011 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2780 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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