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Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties

Autor
Gonzalez, M.; Saéz, Mariel.; Yannick, S.
Tipus d'activitat
Article en revista
Revista
Annali di matematica pura ed applicata
Data de publicació
2014-12-01
Volum
193
Número
6
Pàgina inicial
1823
Pàgina final
1850
DOI
https://doi.org/10.1007/s10231-013-0358-2 Obrir en finestra nova
Projecte finançador
Ecuacions en derivades parcials i aplicacions
Repositori
http://hdl.handle.net/2117/25175 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs10231-013-0358-2 Obrir en finestra nova
Resum
We investigate the equation; (-Delta(Hn))(gamma) w = f(w) in H-n,; where (-Delta(Hn))(gamma) corresponds to the fractional Laplacian on hyperbolic space for gamma is an element of(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-+/- subset of partial deri...
Citació
Gonzalez, M.; Saéz, Mariel.; Yannick, S. Layer solutions for the fractional Laplacian on hyperbolic space: existence, uniqueness and qualitative properties. "Annali di matematica pura ed applicata", 01 Desembre 2014, vol. 193, núm. 6, p. 1823-1850.
Paraules clau
CONJECTURE, Fractional Laplacian, GIORGI, Hyperbolic space, Layer solution, MANIFOLDS, PHASE-TRANSITIONS, REGULARITY, SEMILINEAR ELLIPTIC-EQUATIONS, SYMMETRY, Symmetry
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants