2017
Том 69
№ 9

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Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients

Sun He-Jun

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 7, pp 1154-1164.

Citation Example: Sun He-Jun Estimates for weighted eigenvalues of fourth-order elliptic operator with variable coefficients // Ukr. Mat. Zh. - 2011. - 63, № 7. - pp. 999-1008.

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