Electron. J. Differential Equations, Vol. 2018 (2018), No. 165, pp. 1-14.

Sharper estimates for the eigenvalues of the Dirichlet fractional Laplacian on planar domains

Selma Yildirim, Turkay Yolcu

In this article, we study the eigenvalues of the Dirichlet fractional Laplacian operator $(-\Delta)^{\alpha/2}$, $0<\alpha<1$, restricted to a bounded planar domain $\Omega\subset \mathbb{R}^2$. We establish new sharper lower bounds in the sense of the Weyl law for the of sums of eigenvalues, which advance the recent results obtained in several articles even in a more general setting.

Submitted March 22, 2018. Published September 12, 2018.
Math Subject Classifications: 35P15, 35P20, 60G52.
Key Words: Fractional Laplacian; stable processes; eigenvalue.

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Selma Yildirim
The University of Chicago
Department of Mathematics
Chicago, IL 60637, USA
email: selma@uchicago.edu, selmayildirim@gmail.com
Turkay Yolcu
Bradley University
Department of Mathematics
Peoria, IL 61625, USA
email: tyolcu@bradley.edu

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