Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator

Details Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator Refined Semiclassical Asymptotics for Fractional Powers of the Laplace Operator

2011-05-26

arxiv.org/abs/1105.5181v1

Mathematics

Spectral Theory

33 pages

Scientific paper

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.

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