Geodesic
Estimate of the first eigenvalue of a selfadjoint elliptic operator
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 46-52

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Let $L$ be a symmetric positive elliptic operator o! order m with smooth coefficients in a bounded domain. The problem considered is that of estimating a minimum number $\lambda$ for which the homogeneous Dirichlet problem for the equation $Lu-\lambda Qu=0$ has a non-trivial solution. It is assumed that $Q(x)\ge0$, $\int Q^\alpha(x)\,dx=1$, where $\alpha$ is a real number, $\alpha\ne0$. 
@article{VMUMM_1983_3_a8,
     author = {Yu. V. Egorov and V. A. Kondratiev},
     title = {Estimate of the first eigenvalue of a selfadjoint elliptic operator},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {46--52},
     publisher = {mathdoc},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a8/}
}
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Yu. V. Egorov; V. A. Kondratiev. Estimate of the first eigenvalue of a selfadjoint elliptic operator. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 46-52. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a8/