一类加权Sobolev空间中重调和算子的特征值估计

摘要

This paper considers the eigenvalue problem for the biharmonic equation △2 u -μ w ( x ) u = 0 in weighted Sobolev space W1,p0 (Ω, w (x) ), u= 0 on Ω, whereΩ Rm isa bounded smooth domain, w (x) ∈ L∞ (Ω) is also bounded. For m ≥ 2, three estimates of the eigenvaluesμi, I = 1,… ,n are obtained.%论文讨论了加权Sobolev空间W1,p0(Ω,w(x))中重调和方程△2u-μw(x)u=0,u| Ω=0的特征值估计,其中Ω Rm是边界光滑的有界区域,w(x)∈L∞有界.在m≥2的情况,对μi,i=1,…,n做出了逐步加细的三个估计.