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Boundedness of stable solutions to semilinear elliptic equations: A survey

Autor
Cabre, X.
Tipus d'activitat
Article en revista
Revista
Advanced nonlinear studies
Data de publicació
2017-05-01
Volum
17
Número
2
Pàgina inicial
355
Pàgina final
368
DOI
https://doi.org/10.1515/ans-2017-0008 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/105066 Obrir en finestra nova
URL
https://www.degruyter.com/view/j/ans.2017.17.issue-2/ans-2017-0008/ans-2017-0008.xml Obrir en finestra nova
Resum
This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension 4. They are expected to be true also in dimensions 5 to 9, but this is still an open problem which has only been established in the radial case.
Citació
Cabre, X. Boundedness of stable solutions to semilinear elliptic equations: A survey. "Advanced nonlinear studies", 1 Maig 2017, vol. 17, núm. 2, p. 355-368.
Paraules clau
Boundedness of Solutions, Semilinear Elliptic Equations, Stable Solutions
Grup de recerca
EDP - Equacions en Derivades Parcials i Aplicacions

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