Spectral gap estimate for fractional Laplacian
Probability
2010-04-27 v1
Abstract
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.
Cite
@article{arxiv.math/0606509,
title = {Spectral gap estimate for fractional Laplacian},
author = {M. Kwasnicki},
journal= {arXiv preprint arXiv:math/0606509},
year = {2010}
}
Comments
8 pages