Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties
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Cita com:
hdl:2117/17206
Tipus de documentReport de recerca
Data publicació2012-12
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
where (¿ Hn)
corresponds to the fractional Laplacian on hyperbolic space for
2 (0; 1)
and f is a smooth nonlinearity that typically comes from a double well potential. We prove
the existence of heteroclinic connections in the following sense; a so-called layer solution is a
smooth solution of the previous equation converging to 1 at any point of the two hemispheres
S @1Hn and which is strictly increasing with respect to the signed distance to a totally
geodesic hyperplane :We prove that under additional conditions on the nonlinearity uniqueness
holds up to isometry. Then we provide several symmetry results and qualitative properties of
the layer solutions. Finally, we consider the multilayer case, at least when
is close to one.
CitacióGonzalez, M.; Saéz, Mariel.; Sire, Y. "Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties". 2012.
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