Two new Weyl-type bounds for the Dirichlet Laplacian
Two new Weyl-type bounds for the Dirichlet Laplacian
In this paper, we prove two new Weyl-type upper estimates for the eigenvalues of the Dirichlet Laplacian. As a consequence, we obtain the following lower bounds for its counting function. For $\lambda \ge \lambda _1$, one has \begin{equation} N(\lambda ) > \dfrac {2}{n+2} \ \dfrac {1}{H_n} \ \left (\lambda -\lambda …