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Spectral gap estimate for fractional Laplacian

M. Kwasnicki
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Abstract

A lower bound estimate λ_2 - λ_1 \ge c λ_1^{-d / α} (\diam D)^{-d - α} for the spectral gap of the Dirichlet fractional Laplacian on arbitrary bounded domain D is proved. This follows from a variational formula for the spectral gap and an upper bound estimate for the supremum norm of the ground state eigenfunction.

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M. Kwasnicki. 2006-06-20. Spectral gap estimate for fractional Laplacian. https://arxiv.org/abs/math/0606509

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