loading page

Lower and upper bounds of Dirichlet eigenvalues for Grushin type degenerate elliptic operators in weighted divergence form with a potential
  • Shenyang Tan,
  • Wenjun Liu
Shenyang Tan
Nanjing University of Information Science and Technology
Author Profile
Wenjun Liu
Nanjing University of Information Science and Technology
Author Profile

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.