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Wave extension problem for the fractional Laplacian

Peter Sjögren (Institutionen för matematiska vetenskaper, matematik) ; Jose Luis Torrea ; Mikko Kemppainen
Discrete and Continuous Dynamical Systems. Series A (1078-0947). Vol. 35 (2015), 10, p. 4905-4929.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2015-02-12. Senast ändrad 2015-05-20.
CPL Pubid: 212533

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys

Chalmers infrastruktur