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Some constructions for the fractional Laplacian on noncompact manifolds
dc.contributor.author | Banica, Valeria |
dc.contributor.author | González Nogueras, María del Mar |
dc.contributor.author | Saéz, Mariel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2016-04-01T11:33:10Z |
dc.date.available | 2016-04-01T11:33:10Z |
dc.date.issued | 2015-01-01 |
dc.identifier.citation | 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. |
dc.identifier.issn | 0213-2230 |
dc.identifier.uri | http://hdl.handle.net/2117/85051 |
dc.description.abstract | 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 general noncompact manifolds, where the problem reduces to obtain suitable upper bounds for the heat kernel. |
dc.format.extent | 32 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Fractional differential equations |
dc.subject.other | Fractional Laplacian |
dc.subject.other | non-compact manifolds |
dc.subject.other | hyperbolic space |
dc.subject.other | extension problem |
dc.subject.other | Fourier symbol |
dc.subject.other | singular kernel |
dc.subject.other | heat kernel |
dc.subject.other | hyperbolic space |
dc.subject.other | sobolev inequalities |
dc.subject.other | riemannian-manifolds |
dc.subject.other | conformal laplacians |
dc.subject.other | schrodinger-equation |
dc.subject.other | extension problem |
dc.subject.other | h-n |
dc.subject.other | regularity |
dc.subject.other | operators |
dc.title | Some constructions for the fractional Laplacian on noncompact manifolds |
dc.type | Article |
dc.subject.lemac | Equacions diferencials el·líptiques |
dc.contributor.group | Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
dc.identifier.doi | 10.4171/RMI/850 |
dc.relation.publisherversion | http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=31&iss=2&rank=13 |
dc.rights.access | Open Access |
local.identifier.drac | 17072901 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Banica, V.; Gonzalez, M.; Saéz, Mariel. |
local.citation.publicationName | Revista matemática iberoamericana |
local.citation.volume | 31 |
local.citation.number | 2 |
local.citation.startingPage | 681 |
local.citation.endingPage | 712 |
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