Spectral gap estimate for fractional Laplacian

Details Spectral gap estimate for fractional Laplacian Spectral gap estimate for fractional Laplacian

2006-06-20

arxiv.org/abs/math/0606509v1

Probab. Math. Statist. 28(1) (2008) 163-167

Mathematics

Probability

8 pages

Scientific paper

A lower bound estimate \lambda_2 - \lambda_1 \ge c \lambda_1^{-d / \alpha}
(\diam D)^{-d - \alpha} 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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