Wave extension problem for the fractional Laplacian
Artikel i vetenskaplig tidskrift, 2015

We show that the fractional Laplacian can be viewed as a Dirichlet-to-Neumann map for a degenerate hyperbolic problem, namely, the wave equation with an additional diffusion term that blows up at time zero. A solution to this wave extension problem is obtained from the Schrodinger group by means of an oscillatory subordination formula, which also allows us to find kernel representations for such solutions. Asymptotics of related oscillatory integrals are analysed in order to determine the correct domains for initial data in the general extension problem involving non-negative self-adjoint operators. An alternative approach using Bessel functions is also described.

Författare

Peter Sjögren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Peter Sjögren

Chalmers University of Technology

Mikko Kemppainen

Universidad Autonoma de Madrid (UAM)

Discrete and Continuous Dynamical Systems

1078-0947 (ISSN)

Vol. 35 4905-4929

Fundament

Grundläggande vetenskaper

Ämneskategorier

Matematisk analys

DOI

10.3934/dcds.2015.35.4905