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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

Corresponding Author:[email protected]

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Wenjun Liu
Nanjing University of Information Science and Technology
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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.