The generalised Pólya conjecture for the Dirichlet eigenvalues
Liu, Genqian
Original · EN
In this paper, we prove the Generalized Pólya conjecture for the Dirichlet eigenvalues. In other words, we show that λₖ(α) ≥ (2π)α kα/ⁿ(ωₙ · vol(Ω))α/ⁿ, for k=1,2,3,.... where λₖ(α) is the k-th Dirichlet eigenvalue for the fractional Laplacian (-Δ)α/² with α∈ (0,2] in a bounded domain Ω⊂ Rⁿ.
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