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

Abstract

In this article, we study the eigenvalues of the Dirichlet fractional Laplacian operator (-∆)^α/2, 0 < α < 1, restricted to a bounded planar domain Ω ⊂ ℝ². 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 in a more general setting.