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Some constructions for the fractional Laplacian on noncompact manifolds

Autor
Banica, V.; Gonzalez, M.; Saéz, Mariel.
Tipus d'activitat
Article en revista
Revista
Revista matemática iberoamericana
Data de publicació
2015-01-01
Volum
31
Número
2
Pàgina inicial
681
Pàgina final
712
DOI
https://doi.org/10.4171/RMI/850 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repositori
http://hdl.handle.net/2117/85051 Obrir en finestra nova
http://www.pagines.ma1.upc.edu/~mgonzalez/Papers/Banica_Gonzalez_Saez.pdf Obrir en finestra nova
URL
http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=31&iss=2&rank=13 Obrir en finestra nova
Resum
We give a definition of the fractional Laplacian on some noncompact manifolds, through an extension problem introduced by Caffarelli-Silvestre. While this definition in the compact case is straightforward, in the noncompact setting one needs to have a precise control of the behavior of the metric at infinity 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 gener...
Citació
Banica, V., Gonzalez, M., Saéz, Mariel. Some constructions for the fractional Laplacian on noncompact manifolds. "Revista matemática iberoamericana", 01 Gener 2015, vol. 31, núm. 2, p. 681-712.
Paraules clau
Fourier symbol, Fractional Laplacian, conformal laplacians, extension problem, h-n, heat kernel, hyperbolic space, non-compact manifolds, operators, regularity, riemannian-manifolds, schrodinger-equation, singular kernel, sobolev inequalities
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants

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