Lower Bounds for Laplacian and Fractional Laplacian Eigenvalues

Abstract

In this paper, we investigate eigenvalues of Laplacian on a bounded domain in an $n$-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which gives an improvement of results due to A. D. Melas [15]. On the other hand, for the case of fractional Laplacian $(-\Delta {)}^{\alpha /2}{|}_D$, where $\alpha \in (0,2]$, we obtain a sharper lower bound for the sum of its eigenvalues, which gives an improvement of results due to S.Y. Yolcu and T. Yolcu [23].

26 pages

References in corpus (1)

• Two dimensional Berezin-Li-Yau inequalities with a correction term