Refined semiclassical asymptotics for fractional powers of the Laplace operator
-
Rupert L. Frank
and
Leander Geisinger
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.
Funding source: NSF
Award Identifier / Grant number: PHY-1068285
Funding source: NSF
Award Identifier / Grant number: PHY-1347399
Funding source: NSF
Award Identifier / Grant number: PHY-1122309
Funding source: DFG
Award Identifier / Grant number: GE 2369/1-1
The authors are grateful to R. Bañuelos, M. Kwaśnicki and B. Siudeja for helpful correspondence and to the anonymous referee for his/her help to improve the paper.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
Articles in the same Issue
- Frontmatter
- Refined semiclassical asymptotics for fractional powers of the Laplace operator
- Projective metric number theory
- Pseudo-parabolic regularization of forward-backward parabolic equations: Power-type nonlinearities
- Right simple singularities in positive characteristic
- Discriminants and Artin conductors
- Hilbertian fields and Galois representations
- Simple endotrivial modules for quasi-simple groups
- A reconstruction theorem for abelian categories of twisted sheaves
- Hyperkähler manifolds of Jacobian type
- The algebra of essential relations on a finite set
