Lower bounds for fractional Laplacian eigenvalues
Copyright policy )Lower bounds for fractional Laplacian eigenvalues
In this paper, we investigate eigenvalues of fractional Laplacian (–Δ)α/2|D, where α ∈ (0, 2], on a bounded domain in an n-dimensional Euclidean space and obtain a sharper lower bound for the sum of its eigenvalues, which improves some results due to Yildirim Yolcu and Yolcu in [Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain, Commun. Contemp. Math. 15(3) (2013) 1250048]. In particular, for the case of Laplacian, we obtain a sharper eigenvalue inequality, which gives an improvement of the result due to Melas in [A lower bound for sums of eigenvalues of the Laplacian, Proc. Amer. Math. Soc. 131 (2003) 631–636].
- Jiangxi Normal University China (People's Republic of)
- Nanjing University of Science and Technology China (People's Republic of)
- South China Normal University China (People's Republic of)
eigenvalues, Estimates of eigenvalues in context of PDEs, fractional Laplacian, Laplacian, lower bound
eigenvalues, Estimates of eigenvalues in context of PDEs, fractional Laplacian, Laplacian, lower bound
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