Eigenvalue estimates for a class of elliptic differential operators in divergence form
Abstract
We compute estimates for eigenvalues of a class of linear second-order elliptic differential operators in divergence form (with Dirichlet boundary condition) on a bounded domain in a complete Riemannian manifold. Our estimates are based upon the Weyl's asymptotic formula. As an application, we find a lower bound for the mean of the first k eigenvalues of the drifting Laplacian. In particular, we have extended for this operator a partial solution given by Cheng and Yang for the generalized conjecture of P\'olya. We also derive a second-Yang type inequality due to Chen and Cheng, and other two inequalities which generalize results by Cheng and Yang obtained for a domain in the unit sphere and for a domain in the projective space.
Cite
@article{arxiv.1607.00066,
title = {Eigenvalue estimates for a class of elliptic differential operators in divergence form},
author = {José N. V. Gomes and Juliana F. R. Miranda},
journal= {arXiv preprint arXiv:1607.00066},
year = {2021}
}
Comments
Final version which has been accepted for publication in Nonlinear Analysis