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Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates

Autor
Cabre, X.; Yannick, S.
Tipus d'activitat
Article en revista
Revista
Annales de l'Institut Henri Poincaré. Analyse non linéaire
Data de publicació
2014-01-01
Volum
31
Número
1
Pàgina inicial
23
Pàgina final
53
DOI
https://doi.org/10.1016/j.anihpc.2013.02.001 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/22391 Obrir en finestra nova
URL
http://arxiv.org/pdf/1012.0867.pdf Obrir en finestra nova
Resum
This is the first of two articles dealing with the equation (-)sv = f (v) in Rn, with s ¿ (0,1), where (-)s stands for the fractional Laplacian — the in¿nitesimal generator of a Lévy process. This equation can be realized as a local linear degenerate elliptic equation in Rn+1+ together with a nonlinear Neumann boundary condition on ¿Rn+1 + =Rn. In this ¿rst article, we establish necessary conditions on the nonlinearity f to admit certain type of solutions, with special interest in bounded...
Citació
Cabre, X.; Yannick, S. Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates. "Annales de l'Institut Henri Poincaré. Analyse non linéaire", 01 Gener 2014, vol. 31, núm. 1, p. 23-53.
Paraules clau
DEGENERATE ELLIPTIC-EQUATIONS, DIFFUSION, EXTENSION PROBLEM, INEQUALITY, SPACE
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants