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The extremal solution for the fractional Laplacian

Autor
Ros, X.; Serra, J.
Tipus d'activitat
Article en revista
Revista
Calculus of variations and partial differential equations
Data de publicació
2014-07-01
Volum
50
Número
3-4
Pàgina inicial
723
Pàgina final
750
DOI
https://doi.org/10.1007/s00526-013-0653-1 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/23499 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs00526-013-0653-1 Obrir en finestra nova
Resum
We study the extremal solution for the problem (-¿)su=¿f(u) in O , u=0 in Rn\O , where ¿>0 is a parameter and s¿(0,1) . We extend some well known results for the extremal solution when the operator is the Laplacian to this nonlocal case. For general convex nonlinearities we prove that the extremal solution is bounded in dimensions n<4s . We also show that, for exponential and power-like nonlinearities, the extremal solution is bounded whenever n<10s . In the limit s¿1 , n<10 is optimal. In ...
Citació
Ros, X.; Serra, J. The extremal solution for the fractional Laplacian. "Calculus of variations and partial differential equations", 01 Juliol 2014, vol. 50, núm. 3-4, p. 723-750.
Paraules clau
Semilinear Elliptic-equations, Variational-methods, Positive Solutions, Dimension 4, Regularity, Boundedness, Minimizers, Operators, Inequalities
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants

  • Ros Oton, Xavier  (autor)
  • Serra Montoli, Joaquim  (autor)