Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator
Spectral Theory
2013-05-21 v2 Mathematical Physics
math.MP
Probability
Abstract
We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a two-term formula for the sum of eigenvalues with the leading (Weyl) term given by the volume and the subleading term by the surface area. Our result is valid under very weak assumptions on the regularity of the boundary.
Cite
@article{arxiv.1105.5181,
title = {Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator},
author = {Rupert L. Frank and Leander Geisinger},
journal= {arXiv preprint arXiv:1105.5181},
year = {2013}
}
Comments
33 pages; minor revisions