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

  • He-Jun Sun

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.
Published
25.07.2011
How to Cite
SunH.-J. “Estimates for Weighted Eigenvalues of Fourth-Order Elliptic Operator With Variable Coefficients”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 7, July 2011, pp. 999-1008, http://umj.imath.kiev.ua/index.php/umj/article/view/2780.
Section
Research articles