双调和算子本征值的上界

Upper Bounds for Eigenvalues of the Biharmonic Operator

设Ω是 Rn中的有界区域 ,其边界足够光滑 ,λk为双调和算子在自由边界条件下的第 k个本征值 ,利用变分原理及 Fourier变换 ,给出了本征值部分和 ∑kj=1λj的一个上界 ,该上界仅依赖于区域的体积 .

Under the natural boundary condition, let λ k be the kth eigenvalue of the biharmonic operator on a bounded domain Ω with sufficiently smooth boundary in Rn. By means of the Fourier transform and the variational principle, an upper bound for partial sums ∑kj=1λ j of eigenvalues is provided, which depends only on the volume of Ω.