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Some constructions for the fractional Laplacian on noncompact manifolds

Author
Banica, V.; Gonzalez, M.; Sáez, M.
Type of activity
Report
Date
2012-12
Code
prepr201209GonBS(preprints-2012#9)
Project funding
EQUACIONS DIFERENCIALS EN DERIVADES PARCIALS I APLICACIONS
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repository
http://hdl.handle.net/2117/17931 Open in new window
URL
http://www.pagines.ma1.upc.edu/~mgonzalez/Papers/Banica_Gonzalez_Saez.pdf Open in new window
Abstract
We give a de nition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Ca arelli-Silvestre. While this de nition in the compact case is straightforward, in the noncompact setting one needs to have a precise control of the behavior of the metric at in nity and geometry plays a crucial role. First we give explicit calculations in the hyperbolic space, including a formula for the kernel and a trace Sobolev inequality. Then we consider more general n...
Citation
Banica, V.; Gonzalez, M.; Sáez, M. "Some constructions for the fractional Laplacian on noncompact manifolds". 2012.
Group of research
EDP - Partial Differential Equations and Applications

Participants

  • Banica, Valeria  (author)
  • Gonzalez Nogueras, Maria Del Mar  (author)
  • Sáez, Mariel  (author)

Attachments