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Sharp energy estimates for nonlinear fractional diffusion equations

Autor
Cabre, X.; Cinti, E.
Tipus d'activitat
Article en revista
Revista
Calculus of variations and partial differential equations
Data de publicació
2014-01
Volum
49
Número
1-2
Pàgina inicial
233
Pàgina final
269
DOI
https://doi.org/10.1007/s00526-012-0580-6 Obrir en finestra nova
Projecte finançador
Ecuaciones en derivadas parciales: problemas de reacción-difusión y problemas geométricos
Repositori
http://hdl.handle.net/2117/21782 Obrir en finestra nova
URL
http://link.springer.com/article/10.1007%2Fs00526-012-0580-6 Obrir en finestra nova
Resum
We study the nonlinear fractional equation (-Delta)(s) u = f (u) in R-n, for all fractions 0 < s < 1 and all nonlinearities f. For every fractional power s is an element of (0, 1), we obtain sharp energy estimates for bounded global minimizers and for bounded monotone solutions. They are sharp since they are optimal for solutions depending only on one Euclidian variable. As a consequence, we deduce the one-dimensional symmetry of bounded global minimizers and of bounded monotone solutions in dim...
Citació
Cabre, X.; Cinti, E. Sharp energy estimates for nonlinear fractional diffusion equations. "Calculus of variations and partial differential equations", Gener 2014, vol. 49, núm. 1-2, p. 233-269.
Paraules clau
Energy estimates, Fractional laplacian, Symmetry properties
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

Participants