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Lower bounds of Dirichlet eigenvalues for a class of higher order degenerate elliptic operators

机译:一类高阶退化椭圆算子的Dirichlet特征值的下界

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摘要

Let Omega be a bounded open domain in R-n with smooth boundary partial derivative Omega, X = (X-1, X-2, ... , X-m) be a system of real smooth vector fields defined on Omega and the boundary partial derivative Omega is non-characteristic for X. Denote lambda(k) as the k-th Dirichlet eigenvalue for degenerate elliptic operator L on Omega with L = (Sigma(m)(j=1) X-j(2p))(2), p = 1, then in this paper, we give a lower bound estimate of lambda(k) for the operator L by using weighted Sobolev embedding theorem and maximally hypoelliptic estimate.
机译:让Omega是RN中的有界开放域,具有平滑的边界部分导数omega,x =(x-1,x-2,...,xm)是在omega和边界部分导数ωmomega上定义的真实光滑矢量字段系统X是非特征的。用L =(Sigma(M)(J = 1)XJ(2P))(2),P>,表示Lambda(k)作为emga e椭圆形算子L的k = dirichlet特征值。 = 1,然后在本文中,我们通过使用加权SoboLev嵌入定理和最大低压尺寸估计来给予操作员L的Lambda(k)的较低估计。

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