Lower and upper bounds of Dirichlet eigenvalues for Grushin type
degenerate elliptic operators in weighted divergence form with a
potential
Abstract
In this paper, we consider the estimates of Dirichlet eigenvalues for
Grushin type degenerate elliptic operator in weighted divergence form
with a potential $-{\rm
div}_{G}(A\nabla_{G})+\langle
A\nabla_{G}\phi,\nabla_{G}\rangle-V$.
Using the method of Fourier transformation, we get precise lower bound
estimates for the eigenvalues. Then, through the way of trail function,
we obtain Yang-type inequalities which give upper bounds of eigenvalues.