Some constructions for the fractional Laplacian on noncompact manifolds
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Cita com:
hdl:2117/17931
Tipus de documentReport de recerca
Data publicació2012-12
Condicions d'accésAccés obert
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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 noncompact
manifolds, where the problem reduces to obtain suitable upper bounds for the heat
kernel.
CitacióBanica, V.; Gonzalez, M.; Sáez, M. "Some constructions for the fractional Laplacian on noncompact manifolds". 2012.
Forma partprepr201209GonBS(preprints-2012#9)
URL repositori externhttp://www.pagines.ma1.upc.edu/~mgonzalez/Papers/Banica_Gonzalez_Saez.pdf
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